Rural LITE data: f(M)
DATA
# Load R packages
library(Rcpp)
library(RcppArmadillo)
library(dplyr)
다음의 패키지를 부착합니다: ‘dplyr’
The following objects are masked from ‘package:stats’:
filter, lag
The following objects are masked from ‘package:base’:
intersect, setdiff, setequal, unionlibrary(mgcv)필요한 패키지를 로딩중입니다: nlme
다음의 패키지를 부착합니다: ‘nlme’
The following object is masked from ‘package:dplyr’:
collapse
This is mgcv 1.8-41. For overview type 'help("mgcv-package")'.library(openxlsx)
library(lme4) 필요한 패키지를 로딩중입니다: Matrix
다음의 패키지를 부착합니다: ‘lme4’
The following object is masked from ‘package:nlme’:
lmList# Set Directory
setwd("C:/Users/WooJung/Documents/Rproject/EDPmediationpost/RealDataAnalysis")
# setwd("C:/Users/Jennifer/Desktop/EDPmediation/RealDataAnalysis")
# -------------------------------------------------------------------------
# ---------------------------------- DATA ---------------------------------
# -------------------------------------------------------------------------
# Here are the details for this analysis:
# - outcome: 24 month weight change (spreadsheet 2)
# - mediator - Phase 2 attendance (measured as a percentage) - spreadsheet 1
# - baseline confounders - mostly Table 1 from the paper and previous spreadsheet I sent
# - potential post treatment confounder - 6 month weight (or 6 month weight change) - spreadsheet 4
# - ok to merge control/low and moderate/high arms (so only two arms)
# Load Data
data1 = read.xlsx('RL_WTS_24mo_MD.xlsx', sheet = 'wts24', startRow = 2)
# data1$ID
# data1$CONDITION
# data1$TRTARM
# data1$WTKG_24
# no edu+income data here
data2 = read.xlsx('final_baseline_data_RL.xlsx')
# data2$ID
# data2$CONDITION
# data2$TRTARM
# data2$sex
# data2$race
# data2$AGE_WK1
# data2$HTSV1
# data2$WTKG_SV2
# data2$BMI_SV2
data3 = read.xlsx('tx data att - 082413 - all summary vars.xlsx')
# data3$ID
# data3$CONDITION
# data3$TRTARM
# data3$p2_attmu_tot_pc
#
data4 = read.xlsx('RLITE_LABS_WTS.xlsx', sheet = 'WTS_0')
# data4$ID
# data4$CONDITION
# data4$TRTARM
# data4$WTKG_0
#
data5 = read.xlsx('RLITE_LABS_WTS.xlsx', sheet = 'WTS_6')
# data5$ID
# data5$CONDITION
# data5$TRTARM
# data5$WTKG_6
#
data6 = read.xlsx('RLITE_LABS_WTS.xlsx', sheet = 'WTS_24')
# data6$ID
# data6$CONDITION
# data6$TRTARM
# data6$WTKG_24
# - mediator - Phase 2 attendance (measured as a percentage) - spreadsheet 1
# - baseline confounders - mostly Table 1 from the paper and previous spreadsheet I sent
sum(abs(data2$ID!=data3$ID))[1] 0sum(abs(data2$ID!=data4$ID))[1] 0sum(abs(data2$ID!=data5$ID))[1] 0sum(abs(data2$ID!=data6$ID))[1] 0# we may add education and income
# Just ignore the warning message!
LITEdata = data.frame(id = data6$ID,
cond = data6$CONDITION,
trt = as.numeric(data6$TRTARM),
wgt24 = as.numeric(data6$WTKG_24),
wgt6 = as.numeric(data5$WTKG_6),
wgt0 = as.numeric(data4$WTKG_0),
att = as.numeric(data3$p2_attmu_tot_pc),
sex = as.numeric(data2$sex),
race = ifelse(as.numeric(data2$nih_race_BIQ)==5,1,0), # white no not
age = as.numeric(data2$AGE_WK1),
bmi = as.numeric(data2$BMI_SV2))
# Drop variables with NAs
N = nrow(LITEdata)
sum(is.na(LITEdata$cond))[1] 0sum(is.na(LITEdata$att))[1] 0sum(is.na(LITEdata$sex))[1] 0sum(is.na(LITEdata$age))[1] 0sum(is.na(LITEdata$race))[1] 0sum(is.na(LITEdata$bmi))[1] 0sum(is.na(LITEdata$wgt0))[1] 0sum(is.na(LITEdata$wgt6))[1] 56sum(is.na(LITEdata$wgt24))[1] 121# wgt6: 56 NAs (among N = 612)
sum(is.na(LITEdata$wgt6))[1] 56# wgt24: 121 NAs (among N = 612)
sum(is.na(LITEdata$wgt24))[1] 121# both NA: 37 NAs (among N = 612)
sum(is.na(LITEdata$wgt6)*is.na(LITEdata$wgt24))[1] 37# Total NA: 140 NAs (among N = 612)
sum((is.na(LITEdata$wgt6) + is.na(LITEdata$wgt24))>=1)[1] 140# Delete NAs -> No!
# LITEdata = LITEdata[-which(apply(is.na(LITEdata), 1, sum)>0),]
# Outcome: Weight change between wgt 0 and wgt 24
LITEdata$wgtchange0_24 = LITEdata$wgt24 - LITEdata$wgt0
# Post-treatment confounder: Weight change between wgt 0 and wgt 6
LITEdata$wgtchange0_6 = LITEdata$wgt6 - LITEdata$wgt0
# Post-treatment confounder: Weight change between wgt 0 and wgt 6
LITEdata$trtmerge = ifelse(LITEdata$trt<2.5,0,1)
{
esttype = "mean"
# esttype = "median"
save_cluster = TRUE
# save_cluster = FALSE
# Extract ID for simulated dataset (specific to LSF computing cluster)
# Note: The LSB_JOBINDEX is specified in the bsub command using the -J
# option
run_ID = 1
# Specify the seed so can repeat simulation later if necessary
set.seed(run_ID)
# ------------------------------------------------------------------------------
# Define of constants (adjust to fit the data generating scenario) -------------
# ------------------------------------------------------------------------------
# Define number of observations per draw when using Monte Carlo integration to
# integrate out confounders
D = 1e4
# Define number of Markov Chain Monte Carlo (MCMC) draws in Gibbs Sampler
# Define number of MCMC draws to 'burn' in Gibbs Sampler (check convergence)
# gibbs_iter = 1e5
# gibbs_burnin = 5e4
gibbs_iter = 5e3
gibbs_burnin = 5e3
# the number of MC integration per iteration for a MCMC chain
# gibbs_thin = 10
gibbs_thin = 100
# gibbs_num = 2e3
# gibbs_thin = floor(gibbs_iter/gibbs_num)
# Define number of Monte Carlo draws when using Monte Carlo integration to
# integrate out confounders
# num_MC = 1e4
# num_MC = 1e3
num_MC = 1e2
# num_MC_prior
num_MC_prior = 1e5
rho = "unif"
# ------------------------------------------------------------------------------
# End Definition of Constants --------------------------------------------------
# ------------------------------------------------------------------------------
}EDPM
# -------------------------------------------------------------------------
# ------------------ EDP with a post-treatment confounder -----------------
# -------------------------------------------------------------------------
setwd("C:/Users/WooJung/Documents/Rproject/EDPmediationpost/RealDataAnalysis")
# EDPM
Y = LITEdata$wgt24
M = LITEdata$att
V = LITEdata$wgt6
Z = LITEdata$trtmerge
C = cbind(LITEdata$sex,
LITEdata$race,
LITEdata$age,
LITEdata$bmi,
LITEdata$wgt0)dist. of (Y,M)
set.seed(1)
M = LITEdata$att
library(MASS)
다음의 패키지를 부착합니다: ‘MASS’
The following object is masked from ‘package:dplyr’:
selectlibrary(plotly)필요한 패키지를 로딩중입니다: ggplot2
Registered S3 method overwritten by 'data.table':
method from
print.data.table
Registered S3 methods overwritten by 'htmltools':
method from
print.html tools:rstudio
print.shiny.tag tools:rstudio
print.shiny.tag.list tools:rstudio
Registered S3 method overwritten by 'htmlwidgets':
method from
print.htmlwidget tools:rstudio
다음의 패키지를 부착합니다: ‘plotly’
The following object is masked from ‘package:ggplot2’:
last_plot
The following object is masked from ‘package:MASS’:
select
The following object is masked from ‘package:stats’:
filter
The following object is masked from ‘package:graphics’:
layoutind_naY = which(is.na(Y))
x = M[-ind_naY]
y = Y[-ind_naY]
den3d = kde2d(x, y, n = 200)
plot_ly(x=den3d$x, y=den3d$y, z=t(den3d$z)) %>% add_surface()
plot(density(x))
plot(density(y))
EDPM (Y, M , Z, C)
# -------------------------------------------------------------------------
# ------------------ EDP with a post-treatment confounder -----------------
# -------------------------------------------------------------------------
setwd("C:/Users/WooJung/Documents/Rproject/EDPmediationpost/RealDataAnalysis")
sourceCpp("EDPsource_cpp_realdata.cpp")EDPM (Y, M , Z, C)
```r
# -------------------------------------------------------------------------
# ------------------ EDP with a post-treatment confounder -----------------
# -------------------------------------------------------------------------
setwd(\C:/Users/WooJung/Documents/Rproject/EDPmediationpost/RealDataAnalysis\)
sourceCpp(\EDPsource_cpp_realdata.cpp\)
source(\EDPsource_r_realdata.R\)
# EDPM
Y = LITEdata$wgt24
M = LITEdata$att
V = LITEdata$wgt6
Z = LITEdata$trtmerge
C = cbind(LITEdata$sex,
LITEdata$race,
LITEdata$age,
LITEdata$bmi,
LITEdata$wgt0)
eps = - 0.1
newM = M * (1 + 2 * eps) / 2 + 0.5
newM = log(newM/(1-newM))
# a = (((invlogit(newM) - 0.5) * 2 / (1 + 2 * eps))^{3})/2 + 0.5
# a - M
hist(M)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxucGxvdChkZW5zaXR5KE0pKVxuYGBgXG5gYGAifQ== -->
```r
```r
plot(density(M))
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChuZXdNKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(newM)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxucGxvdChkZW5zaXR5KG5ld00pKVxuYGBgXG5gYGAifQ== -->
```r
```r
plot(density(newM))
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG5NID0gbmV3TVxuXG5NQ01DcmVzdWx0ID0gRURQbWVkaWF0aW9uTUNNQyhZLCBNLCBWLCBaLCBDLFxuICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgZ2liYnNfaXRlciwgZ2liYnNfYnVybmluLCBnaWJic190aGluLFxuICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgRCwgbnVtX01DLCBudW1fTUNfcHJpb3IpXG5gYGBcbmBgYCJ9 -->
```r
```r
M = newM
MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
gibbs_iter, gibbs_burnin, gibbs_thin,
D, num_MC, num_MC_prior)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Bur-In End 5000 Time: Sun Mar 12 23:58:59 2023 Gibbs Iteration 250 ( 5 %) Time: Sun Mar 12 23:59:06 2023 Gibbs Iteration 500 ( 10 %) Time: Sun Mar 12 23:59:15 2023 Gibbs Iteration 750 ( 15 %) Time: Sun Mar 12 23:59:22 2023 Gibbs Iteration 1000 ( 20 %) Time: Sun Mar 12 23:59:32 2023 Gibbs Iteration 1250 ( 25 %) Time: Sun Mar 12 23:59:43 2023 Gibbs Iteration 1500 ( 30 %) Time: Sun Mar 12 23:59:54 2023 Gibbs Iteration 1750 ( 35 %) Time: Mon Mar 13 00:00:04 2023 Gibbs Iteration 2000 ( 40 %) Time: Mon Mar 13 00:00:14 2023 Gibbs Iteration 2250 ( 45 %) Time: Mon Mar 13 00:00:25 2023 Gibbs Iteration 2500 ( 50 %) Time: Mon Mar 13 00:00:36 2023 Gibbs Iteration 2750 ( 55 %) Time: Mon Mar 13 00:00:46 2023 Gibbs Iteration 3000 ( 60 %) Time: Mon Mar 13 00:00:55 2023 Gibbs Iteration 3250 ( 65 %) Time: Mon Mar 13 00:01:06 2023 Gibbs Iteration 3500 ( 70 %) Time: Mon Mar 13 00:01:16 2023 Gibbs Iteration 3750 ( 75 %) Time: Mon Mar 13 00:01:27 2023 Gibbs Iteration 4000 ( 80 %) Time: Mon Mar 13 00:01:37 2023 Gibbs Iteration 4250 ( 85 %) Time: Mon Mar 13 00:01:48 2023 Gibbs Iteration 4500 ( 90 %) Time: Mon Mar 13 00:01:57 2023 Gibbs Iteration 4750 ( 95 %) Time: Mon Mar 13 00:02:07 2023 Gibbs Iteration 5000 ( 100 %) Time: Mon Mar 13 00:02:16 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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-->
```r
```r
{
# Significance Level alpha
level = 0.05
quantile_alpha = c(level/2,1-level/2)
# the number of Gibbs Sampler stored
n_MCMC = MCMCresult$constants$n_MCMC
# Define interation check
iter_check = floor(n_MCMC/10)
M0_mc = list(NA)
Mr_mc = list(NA)
M1_mc = list(NA)
N = MCMCresult$constants$N
D = MCMCresult$constants$D
num_MC = MCMCresult$constants$num_MC
p_V = MCMCresult$constants$p_V
p_Z = MCMCresult$constants$p_Z
p_C1 = MCMCresult$constants$p_C1
p_C2 = MCMCresult$constants$p_C2
f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
a_Ysig2 = MCMCresult$priors$a_Ysig2
b_Ysig2 = MCMCresult$priors$b_Ysig2
a_Ybeta = MCMCresult$priors$a_Ybeta
B_Ybeta = MCMCresult$priors$B_Ybeta
a_Msig2 = MCMCresult$priors$a_Msig2
b_Msig2 = MCMCresult$priors$b_Msig2
a_Mbeta = MCMCresult$priors$a_Mbeta
B_Mbeta = MCMCresult$priors$B_Mbeta
a_Vsig2 = MCMCresult$priors$a_Vsig2
b_Vsig2 = MCMCresult$priors$b_Vsig2
a_Vbeta = MCMCresult$priors$a_Vbeta
B_Vbeta = MCMCresult$priors$B_Vbeta
a_pi = MCMCresult$priors$a_pi
b_pi = MCMCresult$priors$b_pi
a_mu = MCMCresult$priors$a_mu
b_mu = MCMCresult$priors$b_mu
a_tau2 = MCMCresult$priors$a_tau2
b_tau2 = MCMCresult$priors$b_tau2
alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
rho = runif(n_MCMC)
# End initial values ------------------------------------------------------------
for (post_reps in 1:n_MCMC) {
Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
rho_mc = rho[post_reps] * rep(1,D)
YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
ZpiPars_array = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
XpiPars_array = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
XmuPars_array = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
alpha_theta = alpha_theta_draws[post_reps]
alpha_omega = alpha_omega_draws[post_reps]
MCresult = EDPpostmc_concon(p_C1, p_C2,
n_k, n_rk, Ky, Kyx, max_Kx_Sy,
D, num_MC, rho_mc,
YbetaPars, Ysig2Pars,
MbetaPars, Msig2Pars,
VbetaPars_array, Vsig2Pars_array,
ZpiPars_array, XpiPars_array,
XmuPars_array, Xtau2Pars_array,
alpha_theta, alpha_omega,
f0_z0_mc, f0_z1_mc,
YbetaPrior_mc,
MbetaPrior_mc, Msig2Prior_mc,
VbetaPrior_mc, Vsig2Prior_mc,
a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
M0_mc[[post_reps]] = MCresult$M0_mc
Mr_mc[[post_reps]] = MCresult$Mr_mc
M1_mc[[post_reps]] = MCresult$M1_mc
if (post_reps %% iter_check == 0){
cat(\Post-Processing\,post_reps,\(\,(post_reps/n_MCMC)*100,\%)\,\Time:\,date(),\\n\)
}
}
distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Mon Mar 13 00:02:17 2023 Post-Processing 10 ( 20 %) Time: Mon Mar 13 00:02:18 2023 Post-Processing 15 ( 30 %) Time: Mon Mar 13 00:02:18 2023 Post-Processing 20 ( 40 %) Time: Mon Mar 13 00:02:19 2023 Post-Processing 25 ( 50 %) Time: Mon Mar 13 00:02:19 2023 Post-Processing 30 ( 60 %) Time: Mon Mar 13 00:02:19 2023 Post-Processing 35 ( 70 %) Time: Mon Mar 13 00:02:20 2023 Post-Processing 40 ( 80 %) Time: Mon Mar 13 00:02:20 2023 Post-Processing 45 ( 90 %) Time: Mon Mar 13 00:02:21 2023 Post-Processing 50 ( 100 %) Time: Mon Mar 13 00:02:21 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTTBfbWMgPSB1bmxpc3QoZGlzdE0kTTBfbWMpXG5Ncl9tYyA9IHVubGlzdChkaXN0TSRNcl9tYylcbk0xX21jID0gdW5saXN0KGRpc3RNJE0xX21jKVxuXG5tZWFuKE0pXG5gYGBcbmBgYCJ9 -->
```r
```r
M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)
mean(M)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDEuMDE5MlxuIn0= -->
[1] 1.0192
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTBdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==0])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDEuMDI2Nzk4XG4ifQ== -->
[1] 1.026798
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTFdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==1])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDEuMDExMDM1XG4ifQ== -->
[1] 1.011035
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# n = MCMCresult$constants$D
n = 1e4
ylim_CE = c( 0.0, 2.0)
xlim_CE = c( min(M) - 1, max(M)+1)
# print(\dist. of M based on the data\)
plot(density(M),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(M[Z==0]),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M[Z==1]),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Data\,col=\green\)
legend(\topright\, legend=c(\M\, \M[Z==0]\, \M[Z==1]\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# print(\dist. of M based on the G-computation\)
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)]),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)]),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)]),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\G-computation\,col=\green\)
# abline(v = 0, col = \black\, lwd = 2)
# abline(v = 1, col = \black\, lwd = 2)
legend(\topright\, legend=c(\M0\, \Mr\, \M1\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
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IvSonjyZ5seY4q9SnFMwGq6nb91MuuGHo7/WO2831pyrb2GAqnqdv5+VZ2FL/+32qF/6rN743IeLnnJp4YCqep2/tbJrBpa7dUPxqeUqlcsLXq5koYCqep2/tbJLIP5jWpFWp2NL08iVRc1LXq5koYCqep2/tZn4ccvkx/9qUznvWXv3qShQKo6nb/VsvNa4/3vJqeUDpe984iGAqnqdP5WF4F+MG7ouXrfvjylNNmn3/gYU+xVimMCVtPp/B3tsdcNLS8LHS8/lx4O1VAgWZ3O3/Gy83C0DJ0sP5ceDtVQIFmdzt/xsrNq6LXB9JTSOK7tNBRIVZfzd7LsPBwlc7z8rP7D4jez11AgVTnMXw0FUpXD/NVQIFU5zF8NBVKVw/zVUCBVOcxfDQVSlcP81VAgVTnMXw0FUpXD/NVQIFU5zF8NBVKVw/zVUCBVOcxfDQVSlcP81VAgVTnMXw0FUpXD/NVQIFWdz9/D8b2UGh+Vb2k/9rs3Zz4saSiQqq7n7/R+dKXqHiAzb2FfPjL/bswaCqSq6/k7ui/yqJr1MrQRzVtFy7sxayiQqq7n72jlWe+uj280P47ml/Uidf7mdBoKpKrr+VsuNN8aN3T0wSiaD3/15pGjo6c+xhR7leKYgNV0PX+He+9nfzrqZLkMffL90Qfjgrbc4FNDgVR1PH/LU0pf+/tRNstl6B//YBTN0aHRtpvTaSiQqo7nb7n0fOrTeve96uk/jM7D1+fr/+jN0Z0/NzbGFHuV4piA1XQ8f8tTSufu1Q0t/+/yrdHCs4zrdz4p//ORw6EaCiRryfzdi1n648pkXi5Lea1aeZ794HC08Pznt37UuOH8ymNcW4q9SnFMwGo6nr9lMq+VDb1c9fJcHdKZ/zx/hb2GAunqdv7Wyawbejj+43ThWR0UPXI4VEOBZHU7f7+qzsKX/3u5flHnvZmFZ3UB/vwV9hoKpKvb+Vsns2potVc/uDVzLVP74VANBZLV7fytk1k29BvVinRu5/1W6+FQDQWS1e38rc/Cj18mP/rTZOe9KuqRK+w1FEhXp/O3iuS1xvvfzZ5Smi3qZsaYYq9SHBOwmk7nbxnJsx+MG3pufuf9XtsbjpzyGFPsVYpjAlbT6fwdnTOqG1rW8nBm533B4VANBZLV6fwdR/JwtAydO6V02H44VEOBZHU6f8eRPBy90/LsAdDqo6NX2GsokK4u5+9k2Tl+Sefs9aDtbzgy0FAgXTnMXw0FUpXD/NVQIFU5zF8NBVKVw/zVUCBVOcxfDQVSlcP81VAgVTnMXw0FUpXD/NVQIFU5zF8NBVKVw/zVUCBVOcxfDQVSlcP81VAgVTnM33wa+uDDb50/f+EPf7neV+XwHADtcpi/iTf0wWsHL35c/enz/fpGUcUzH295TEBHcpi/iTf0/gvFI++Vf7hTTDz63nbHBHQkh/mbSUOH/188+s7wDzeGy9HH1liJ5vAcAO1ymL+ZNPT6pJzlPv3LWx0T0JEc5m8eDX3wyjScw5w+vtUxAR3JYf7m0dDJYdFBtRB9ZPUjojk8B0C7HOZvfg1t/nkrYwI6ksP8zaOhw315DYXeyWH+5tHQwZ3izBujh+6sdWI+h+cAaJfD/E2/oUXxey++fvNK8Xz9SHl66fmtjgnoSJGD09zeU/xeI1VDa/UO/Ee/X6yzK6+hwEYl3tDB4Oaffmt/2tCyqWfWuDxUQ4GNSr6hlY+GIR039NE3jv30Bg0FNimPhk48+LN31/sCDQU2KbOGri3FMQG7Q0MB4jQUIE5DAeLya+j9i+cveK0nkIYMG7rk9fKbfQ0BwLzdauhRGgpsUn4NHdy9uca9PTUU2KQMG7qWFMcE7A4NBYjTUIA4DQWI01CAOA0FiNNQgLjEG/rgtYMWL7onHZCGxBvauJ9Sg9cpAYlIvKGDn+9rKJCu1Bs6+Hy/OPPSzVle6wkkIvmGlhF9bPXjn/M0FNik9Bs6uFMUz4e/WEOBTcqgoYMrxZm17ofcpKHAJuXQ0PsvFI9Hv1ZDgU3KoaGDGwd/ED0iqqHAJmXR0BNIcUzA7tBQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjLoqF3rx5cPD904eDSL9f8Ug0FNimDht74ZtFw5qUUxgRQSb6hD14p5jz28bbHBDCSekOrhF54fbQLf/fDi2tGVEOBTUq9odeHe+8vNx+4sV8Uz6/+9RoKbFLiDS2XoXPFvL7WQlRDgU1KvKH3XyjOvDH70Of7xSPvrfwNNBTYpPQbOh/MloeW0FBgk9JvqHUokK7EGzq4cuR46PCRx1f/eg0FNin1ht4piuK5ximkB98bPvDy4s+fp6HAJqXe0HLZWRRPX3rn5tBHV1/dL9ZahmoosFHJN7S8lmnWs9sfE0At/YYOvni1WdBn3k1hTACVDBo6dPcXV187OHjx0vfXfdsmDQU2Ko+GxqU4JmB3aChAnIYCxGkoQFx+Db1/8fwFr/UE0pBhQ5e858j8paRDnYwJ6KvdauhRGgpsUn4NHdy9ucZVohoKbFKGDV1LimMCdoeGAsRpKECchgLEaShAnIYCxGkoQFziDX3w2kGLFz8+/is3NyaAicQbev+Flpdvep0SkIrEGzr4+b6GAulKvaGDz/eLMy/dnOW1nkAikm9oGdHHVj/+OU9DgU1Kv6GDO0XxfPiLNRTYpAwaOrhSnHkj+rUaCmxSDg29/0LxePRrNRTYpBwaOrhx8AfRI6IaCmxSFg09gRTHBOwODQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiMunoQ8+/Nb58xf+8JfrfZWGApuUeEMfvHbw4sfVnz7fL2rPfLzlMQFMJN7Q+y8Uj7xX/uFOMfHoe9sdE8BEJg0d/n/x6DvDP9wYLkcfW2MlqqHAJmXS0OuTcpb79C9vdUwAE3k09MEr03AOc/r4VscEMJFHQyeHRQfVQvSR1Y+IaiiwSfk1tPnnrYwJYCKPhg735TUUSFAeDR3cKc68MXrozlon5jUU2KT0G1oUv/fi6zevFM/Xj5Snl57f6pgAJnJoaK3egf/o94t1duU1lIa91W17qGQj8YYOBjf/9Fv704aWTT2zxuWhGtpbJwyjmLKi5Bta+WgY0nFDH33j2E9v0NCeOfX26SjL5dHQiQd/9u56X6ChfbFqOr8+Z+XvfeIRspsya+jaUhwTp22FxC1s5sox1VFaaShZO36JuOpyc5WUWpByhIaSsVXyeXs9R7/m6A/VUaY0lDwtXRKO1pRH+7eimQVpW0qdtGcsv4bev3j+gtd69l17vsbLyJVOFB1n/hstWpIKac9l2NAlr5cvjupkTHSrrVujfJ7yT2rpqH17ZuxWQ4/S0B1zdOU3Xnuedj4n5r992xECC9L+yq+hg7s317i3p4bulCP5vL3JeM5qhLR1OWpB2lMZNnQtKY6JoJlCbWbf/TiNJWn7CSsL0t7RUHIwk6ZOl59tJqf9W5ejFqT9oqGkr1Gk7Sw/2y09DquifZFFQ+9ePbh4fujCwaU1DoVWNDR/jRolk8+mRYOyW98PGTT0xjeb1yqdeSmFMdGZcYaqBeh2h7LQksWxiu685Btavm/9rDXuBKKhWZss5LZ9/HMliwapojsu9YZWCb3w+mgX/u6HF9eMqIZma7oAvZ18P8faF8t26nda6g29Pv++9Tf23U+pD5oL0FwKWlp4zYCK7qrEG9pyB7rr7uu542Z24bc9mJCFy9EtjIVNS7yh91+Y3hR55PN9r/XcZeN85rQL36Z1OaqiOyj9hs4H0+vld1muu/Ct2v4VUNGdk35DrUN7o97ZzX0BOuvoPwYqumMSb+jgypHjocNHHl/96zU0E/Ux0OrFkztU0JG5jjowulNSb+idoiiea5xCevC94QNr3GBeQ7OwU7vwbebPMqno7ki9oeWysyievvTOzaGPrr66X6y1DNXQDOziLnyrmX8gVHRXJN/Q8lqmWc9uf0ycnsYSdNtD6UJjpS2iuyH9hg6+eLVZ0GfeTWFMnJLMLwSNmF6FL6I7IYOGDt39xdXXDg5evPT9dd+2SUNTlvul9GHjezA7ubQL8mhoXIpjolL3Y2fPIh2nevfmMqPbHggnpKFsxbig2x7HFlVvgq+i2dNQtkBBa/WtRPb2ev8XkTMNpWt7CjpV35JpWFF/HbnSULo1OQy67YGko8zo8K/F30meNJQulQXt61mkZcqKDqzNs6ShdKgqaPv9hPvu9u29uqI6mhkNpTPVUT8FXWRUUQc6MqOhdKQs6G0FXaas6DijWx4KK9NQOlEXdNujyIGKZkZD6YCCrmOv/ptS0TxoKBunoGvau11fNiqiOdBQNqm6R6fDoOsavaOqpWgONJTN2XMtU9T41igqmjwNZVMU9GRGi1EVTZyGshF79YsXFfQkVDQHGsoGWIKekklF/VUmS0M5dQp6ikbvLqqiydJQTpmd+NM1fo9mf6WJ0lBOU30Y1LVMp2ryyiV/rSnSUE6PnfgNaVTUX25qNJTToqAbNH1LJ3/BidFQTofDoBu2Z5c+TRrKKXAYtBPjig78RSdEQzkxO/GdGd2NanRjZVKgoZxQfQsLU7oje5P7LvkrT4OGciKjKW06d2dvdGM/FU2DhhJXzmYvRNyCyWJURbdPQ4mq353NG2JsRaOiMrpdGkqMgm7Z+FbKFqNbpqFEVDvxCrpdo5P0KrpdGsraxodBFXTbxhWtrs0V0u3QUNZkJz4lozd1slO/PRrKWvaqe04qaDLGb41np35bNJQ17FW3PlfQpDQr6gW33dNQVrVXFdRh0PTsTTPqjV86p6GsptyJtwRNVqOi1XJ0eyPpHQ1lFXbik9esqKeqQxrK8RQ0C/MVtVPfCQ3lGA6D5mNvPqMqunkaylIOg2bmyGLUU7dhGsoSduIzNFtRuxCbpqEsZCc+U/MV9a/gJmko7caHQbc9DiL2ji5GHRrdEA2ljcOg2WurqIxugIZylMOgO6HlwKiKnj4NZcbenmuZdkfLgVEVPW0aSkM9525bgu4MB0Y3TkOZGBXUO9vtltZdeiE9NRrKSDXVvDfoLmq91klFT4mGUtob3+FMQXeSim6OhrK3N725Gbuq5cCoGyufCg3tu/HUUtCd1/oiUBU9KQ3ttfHixC58P9il3wAN7a29PUvQ/llQURmN09Cemr0dJP3RemB04GqnMA3tn73pCnTgSqY+ajkwaqc+TEP7Zu7mZdsbCFt0ZJfeTn2YhvZIcwE6sBPfbwsqajG6Ng3tjblJo6B9d+TAqKudQjS0J2bni8OglFoXo96VZD0auvvmduEdBmWqpaLernk9Grrr3FuHpRZU1GJ0VRq6247eKVdBmdNyYHTgtsor09BdNl9Qe2i0a62ofZaVaOjOOnIQVEBZbGFFZfQYGrqjXMnEmhZU1O/OMTR0BzkPT0j7gVHH0ZfT0F3T/pYSsJJFi1GXFC+kobvlyC6833zWs7Ci/jVup6G7xC48p2BZRf1SHaGhu6P5q+/2nJzAkZe2Tdy+bTk6R0N3xNw7Mvk956QWVtS/zzM0dAc0Fw3lL7jfcE6FnfpVaGj2LEDZmGU79ZajNQ3NW+OuHn6n2YxFy1G/cRUNzVdziWDfig1aVtHe/+JpaK4sQOmQnfqFNDRDzd9n6wA6s3w52u1Y0qGhmZnfgd/mWOidxWfq+3tBiIbmpHkGqa+/sWzXMTv1Pfyt1NBcWICSjMU79T08y6ShGWj+09/7I/gkYelytF+/oxqavPlr6Hv020najjk62pNfVQ1Nmh14krZwNVotR/vxO6uh6Wr+evbhd5E8LczoeLd+x395NTRNFqBkZPFytFzzGKUAAAmYSURBVAcLUg1NjivoydHiilYd3d1fZg1NjOUnuVp8rn4wWo7u5G+1hqZj+iu4q/9is/uO6+juLUg1NA3T37zy96v6Fxsy1a8FqYamYHoFvX6yI5aFdKcWpFk09O7Vg4vnhy4cXPrlml+afEPHv2lf//pu/EJBwzEnmnZiQZpBQ298s2g481IKYzodzXxafrKTlu3W78aCNPmGPnilmPPYx9se0yloLj/lk9229PhoY0Ha2YBOVeoNrRJ64fXRLvzdDy+uGdEUG9pcfm57LNCRFRakeU6J1Bt6fbj3/nLzgRv7RfH86l+fVEP3an19n0V6b4UFaX5zI/GGlsvQuWJeX2shmkZDR/Ecv5tNZr8jcJqWd3SQ3Zs+Jd7Q+y8UZ96Yfejz/eKR91b+Bltt6N6eeEKL8cRY4nYuMyb9hs4Hs+WhJbbR0Gk6B+IJi62Q0tFVKwmfeE2/odmsQ5vpnFzvKZ5wnGNTOppLaaY08YYOrhw5Hjp85PHVv76LhkonnILZVUiLyexKKqWpN/ROURTPNU4hPfje8IGXF3/+vM02dPKMp/nkQpbyimnqDS2XnUXx9KV3bg59dPXV/WKtZeimGjp5ihN6KmHXrB7TLe75Jd/Q8lqmWc9uc0yjp7Tx76B6wqYdG9Mt5jT9hg6+eLVZ0Gfe3caYJk/htv/Ng147NqaT1zt1Nk8zaOjQ3V9cfe3g4MVL31/3bZtOOCbphDTt7R2T085imkdD40Jjun27mc7THhJwmvbmHPmERkw3MKE1tGm67tzQcIBNm29qs6u3Z3t6Gk3V0IF0wq5b1NWjTV37W/e5oc2jnZ0NCEhDW1fnk7rCt8mvofcvnr+w/ms92/66hBOY0RaKRjLa0pphQ5e858j8paRF8T8ANukU67b9hh6V4vEFYHfktw4d3L25xlWiGgpsUoYNXUuKYwJ2h4YCxGkoQFwWDb179eDi+aELB5fWfcG8hgKblEFDb3yzebHSmZdSGBNAJfmGlndHnrXGnZE1FNis1BtaJfTC66Nd+LsfXlwzohoKbFLqDb0+3HufuX3Sjf0jd6lbRkOBTUq8oeUydK6Y19daiGoosEmJNzSn+8sDPZR+Q+eD6fXyQDrSb6h1KJCuxBta3l7++SOPrHGDeQ0FNin1ht4piuK5ximkB98bPvDy4s+fp6HAJqXe0HLZWRRPX3rn5tBHV1/dL9ZahmoosFHJN7S8lmnWs9sfE0At/YYOvni1WdBn3k1hTACVDBo6dPcXV187OHjx0vfXfdsmDQU2Ko+Gxh29Sx3AKTrNXp3i9+pe3qOPs9290tPNzmW7MxnmAnmPPs5290pPNzuX7c5kmAvkPfo4290rPd3sXLY7k2EukPfo42x3r/R0s3PZ7kyGuUDeo4+z3b3S083OZbszGeYCeY8+znb3Sk83O5ftzmSYC+Q9+jjb3Ss93exctjuTYS6Q9+jjbHev9HSzc9nuTIa5QN6jj7PdvdLTzc5luzMZ5gJ5jz7OdvdKTzc7l+3OZJgL5D36ONvdKz3d7Fy2O5NhLpD36ONsd6/0dLNz2e5MhrlA3qOPs9290tPNzmW7MxnmAnmPPs5290pPNzuX7c5kmAvkPfo4290rPd3sXLY7k2EukPfo42x3r/R0s3PZ7kyGuUDeo4+z3b3S083OZbszGeYCeY8+znb3Sk83O5ftzmSYAEnSUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjbgYZeKZ7f9hC69OHFoiguvL7tYWxFz57qoS9e/WYvn+4HfzLc7jPPvLvtcawi/4beKfo0sR78u6L27MfbHkr3+vVUl66Pnu3i0fe2PZROffH7Gf2aZ9/QO/u9mlhXxpOqeHzbQ+lcz57qQSOhRfFYBjE5NfdfyOnXPPeG3hjOqx5NrM+Hm/vcx9Vq9Mwb2x5Mx3r2VA/qZ/vZXw53Pr7Xsy0frhQe/deDXH7N827oF69W/1b159frynhjr2fxL/Qp6t1TPaie5NH23unVQnS4DH2kPnYx/Bt4ecuDOV7WDb0+/Hf60X/fo4k1/eV68Mr4T/3Qu6e6dGXyHPfr6b7T/Lcj/Wc864ZeKc784cdZ/DWfkuHO3Xj1mcW/0Kend0/1nCt9aujUFfvyG3alPFjUp4l1ZxrOOz1raN+e6ln9WoeOffRqFkessm5opU8Tq7H4HC5Je7PZY316qmfdySImp6o6N3/mX217GCvQ0Jxcn+7aaGiPDHuSwT7t6SovSigP4Gx7HMfT0JxcmWlo31YmvXqqm4Z78v3b8M/PP30+jxcXaGhONLQ3T3VDmdAeXdnU8OBKDlueW0PHr2CYHmHv08SyL9+7ba5f95h+SDaj/Ocj+VOnGpoT55R6t83Vy7Me72lC83jKNTQn/b22qdKnp3rset9enDUrh0NWuTX0qD5NrMbi83r/ztT26qkeKV8x/tK2B7FFOexuaWhOhqvw0ZGxXl503aenula++UYW76F5qhqHrK5n8JRraFb6+54jpV491aXr/TybNH2HleEyNP3dLQ3NSvVuaD1977uePdWD5m5Hv5Rn4x99p3wz+/0clgoampc+vwdzz57qmbdgLnp1CrF6jVI27z2toXlxL5D+KJdj/WzoNKIZJFRDs9Pje9L17Klu3BGjbw2t70mXya95/g0F2B4NBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI01CAOA0FiNNQgDgNBYjTUIA4DQWI+/+5dLHZgOoqFgAAAABJRU5ErkJggg==" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDUwKVxuaGlzdChNLDIwLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 50)
hist(M,20,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTBdLDIwLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0wXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==0],20,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==0]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTFdLDIwLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0xXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==1],20,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==1]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDM1MClcbmhpc3QoTTBfbWNbd2hpY2goKE0wX21jPnhsaW1fQ0VbMV0pKihNMF9tYzx4bGltX0NFWzJdKT09MSldLDFlMyx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE0wOiBHLWNvbXB1dGF0aW9uXFwpXG5gYGBcbmBgYCJ9 -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M0: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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xRnAgCLYq8UZwIAi2KvFGcCAItirxRnAgDL/L1yu+YeCQBGUuyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgUeyV4kwAYFHsleJMAGBR7JXiTABgidarDy8uHt3duHfx7M8jf5SGAkhFpF69+sJ5zr5XmAkAJhelVzdPXM/tt3PPBAARxOhVkdB7z6un8B9ePzoyojQUQCpi9Opq8+z9sX/Bq3Pnvh7/8zQUQCoi9Gr7MLRXzKujHojSUACpiNCrjw/d2Y/di96du89+G30DNBRAKuI0tB9M46I9aCiAVPA4FADCxejV5c7roZtL7oz/eRoKIBUxenXtnPvKewvp5qfNBY+Hr99HQwGkIkqvLrcfq//y2cs3G3+8eHrujnoYSkMBJCNOr676v6f0YP6ZAGB6kXr1/qlf0Pu/KswEAJOL16sPv7/44eLi22e/HHvaJhoKIBmKvVKcCQAsir1SnAkALJyDGQDCcQ5mAAjHOZgBIBznYAaAcJyDGQDCcQ5mAAjHue8AINz852Duv/20Mf1MABAFj0MBIBznYAaAcJyDGQDCcQ5mAAjHOZgBIBznYAaAcJyDGQDCKfZKcSYAsCj2SnEmALBE69WbN/6nm364+JbflwewPHF6Vb6ldOt5/fW+3/U81UwAML0ovXp33jv1Mg0FsEwxerUppnNfXvxl+1D0t/oSGgpggWKdg3l70pH3T1yVThoKYJminoP55rJ6Ok9DASxT3HPf3VQnbKKhAJYp8jmYq8ekNBTAMsU+j335oJSGAlimOK+Heuexv96+r0RDASxTpPfl73S+uv3/aCiARYrRq+1H7L3z2G8i+rmjoQCWKEqvtqdg9ppZnJGZhgJYoDi9+mf373i+OqehABYpUq9uXnfO03Tz8zkNBbBAir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJACyKvVKcCQAsir1SnAkALIq9UpwJCXLsSYhPcS9TnAkJoqE4AcW9THEmJIiG4gQU9zLFmZAgGooTUNzLFGdCgmgoTkBxL1OcCQmioTgBxb1McSYkiIbiBObfy9yuuUfCMrAn4QQU9zLFmZAgGooTUNzLFGdCgmgoTkBxL1OcCVLGveBDQ3ECinuZ4kyQ4lY0FCIU9zLFmSCFhkKG4l6mOBPiCMzcYEM7T/JpKE5AcS9TnAlxTN7QFQ3FaSnuZYozYVp13mgoUqe4lynOhGlN0dDdN+c3l9BQnJjiXqY4E6Y1SUN3HozSUJye4l6mOBOmFbOhzW3uu3H6ioko7kmKM2FaNBRLobgnKc6EaX1aQx0NhQzFPUlxJkwr1YaSXvQp7hKKM2FaNBRLobhLKM6EaR3T0N3r0FDoUNwlFGdCMDM7Rza091HQvQ11XkOHb52GYiKKu4TiTAg2SUNXNBSiFHcJxZkQbLKG+nGkoVChuEsozoQAZXBGNHR/mZqGrmgo9CjuEoozIQANRQYUdwnFmRBg2oY6GgpFiruE4kwYo1eYwIb2T6O801A3oqHOfUJDh79JQ9GnuEsozoQxaCjyo7hLKM6EMSZvqAtrqKt/0PW/PzTq3vUY9R3kSnGXUJwJY0RvaH11GgoZiruE4kwYg4YiP4q7hOJMGCNmQ92ehtaxHGio6y5tXV5h/HqM+g5ypbhLKM6EMTqFca7OmXGVtmpVJXs/1n4xqqGrupl2Q1e9hq5oKCajuEsozoQxdhu6U6vDDd35hCcNhTLFXUJxJowR2NAmjcV/DzbUHdHQ+ia7C6ehmI7iLqE4E8awGuqMhrYX1sFz625D2297abQaWl5jVEObm6WhmJDiLqE4E8aYo6ErGopZKe4SijNhjM5rm5/W0OaVz6ka2t4oDcWUFHcJxZnQ6GWk+576/oZWGes+0Ow2tK7gqrp8fENdu0Czoe0oBxraz/6elQcke6U4Exqf0tD28eKohvYeXh5oaPufT2zoioZiPMVdQnEmNEIb2o1i8wplaEPbkHbyOdRQR0MRh+IuoTgTGmENLcvWPuf2XvtsH4w6t9tQ7yl6WEOd+4SG9q9GQ9GnuEsozoRGYEPbKLZvvPcburIa2v3PmoZCi+IuoTgTGhM11Dmroc5rqPmfNQ2FFsVdQnEmNHYbWrdpuKG7Dyz993nCG2o/VjUa6mgoIlHcJRRnQsNo6IqGIluKu4TiTGik1dDejZWTdd/p6q8XDcUxFHcJxZnQ2GmoU27oznfWnYZauRzXUGqKkuKOoDgTGjTU/A5ypbgjKM6ERuINbX6m/tfu4DQUR1DcERRnQiNOQ3vhPEFDXd1QV8+43vPgdOdrGoqS4o6gOBMacRrab138hq6ahq5oKMIp7giKM6HhxaMNlf91880TNNT+z6c31Lmdle19TUNRUtwRFGdCY6ChVZ/qbzsXp6H+7QY2tHfhcEObS6yVp6EoKe4IijOhMdTQVbehXgonbeiob9NQnEy0HeHDi4tHdzfuXTz788gfZeeUVudlbTW0qk9KDXXTNtQR18xE2t6vvnCes+8VZsI09ja0esly3WldCg2tvlfMPthQ50Y0dMX+m5co2/vmieu5/XbumTCVhTZ0NaahKxqKvhjbu0jovefVU/gPrx8dGVH2QWmTNdTFa2iz1E9vqN9KGopdMbb31ebZ+2P/glfnzn09/ufZB6XVny9a+w11/h/ccG5cQ+tvT9/Q4ds91NC27L2GOkdDYYmwvbcPQ3vFvDrqgSj7oLTDDV3RUOQjwvb++NCd/di96N25++y30TfAPihg+N3l8IYOVFCsoc3QTUPbdaWh2BGnof1gGhftwT4o4IQNtaKo0NB6tG5D/cel5t1DQzPD41CYTtjQ4EjGb2h9O2saiiExtvflzuuhm0vujP959kEBhxtafYLIa2ibI4mGWlekoZhajO19vdnPvvLeQrr5aXPB4+Hr97EPCjjc0JV6Q83v0FBMLMr2vtzuaV8+e/lm448XT8/dUQ9DaaiCKhFGKcY0tBuzWG8aRW2o8/+1pqEYEmd7X7meB/PPhKP0G9p7Q3r5De1+h4ZiSKTt/f6pX9D7vyrMhGPQUBqKUeJt7w+/v/jh4uLbZ78ce9omGqpgoKGuisgiGzr87fVxDR1+MRnLo7ixFWfKzlBDVzR03b1n+nfcTkMp6rIpbl7FmbJDQ2koRom2eTkHc9p2G+qaiqwzbWh9peo3CwbuuKahrn8fYpEibV7OwZy6phXt16t9Dd0Xs4QaOvjTXkPr+6GJZPeOaxu6oqE5iLJ5OQdz+upWZNbQwe+YDbXegqehuYmxeTkH8wLsa6ircrNu/5ljQ93ohlLRJYuxcTkH8wKYDe39x7xQvKEHvj2yoV5Nyzunuouco6HZibBxOQfzEiy1oaE/OKqhKxqaoQgbl3PfLUFTld7XGTe0s+I0FJU4DT3mHMxu1/Qz4VhNVXpfhzSJhrJLLxiPQ2GioTQUo8TYuJyDeQFoKA3FKDE2LudgTlz1izhNQ/2vQ5pkXTG1hnZWovMpJ+f2N7S+F7FQUTYu52BO29QNPWUkT7LY3idFaWjW4mxczsGcEv8I32kmDT2uoc5uKBVdrkiblnMwJ4SGHvttq6Hdbxf3pddQTsy8XPE2LedgTgUNpaEIp7hpFWdaMhpKQxFOcdMqzrRkNJSGIpziplWcacloKA1FOMVNqzjTktHQ8G+v67MB0tBsKW5axZkWxwtnv6Gu11BHQ2koBiluWsWZFoeG0lBMIsKmvfnhwvAt5w+VYjfUVWjoNA2tXyg92FA+g5+uCJvu40Nn4LxNWnrhrP+36sBOQ+VjNtNizYY6GpqTGJvun+duFw3VYjXUT0CTDRpKQ7FPlE337tydff+m64jfVmJ3OgEaOs23hxvqBhpq5pKGpivOpttE9Ki/htzF7nQCNDRuQ+t/WQ01gklD0xVp010f9Yc8e9idToCG0lBMItamu9z5eyDjsTtF4pz5jLI+qGnoCRrqymvvbpq4mx7xxNp0Hx8eddrlDnanSJz9qlx9UNPQUzS0un/7m4adPlnRNt2ri38JfUWU3SkSGkpDMTnFTac40yLsNNQ1B3n17SYBNDRKQ5tv72wadvpkKW46xZkWYW9D7QTQ0JG3S0OzpbjpFGdaBBpKQzE5xU2nOFO6XHvMulV5bK+d6zfUDSTANT+RSMxoKE5McdMpzpSUzgFZHcnVP4vfnikb6j8C7SfBa2griZgl09DqNWjndjcZkqK46RRnSsqkDU0sZqk1dEVDU6e46RRnSkZ51PoX7Da0PsbLg99qaBuM1GIm0tDm2vsb6n3jpHsJJqS46RRnSsYxDa0O50XFbK6GDn17oKHFf2joIihuOsWZkkFDtW6Xhi6e4qZTnCkZAw0tj2Yamm5DHZkVpbhdFGdKRq+h9ZHsVjR0ltttGlr/O7ih/EkmUYrbRXGmZNBQrduloYunuF0UZ0rGnoY6GkpDMTnF7aI4UzJoqNbt0tDFU9wuijMlg4Zq3e7hhnqfuG83mrFhaagoxe2iOFMyhhvqaOgMtxvQ0GI77YSUhqpS3C6KMyWDhmrdbnhDVzQ0DYrbRXGmZHgN9Q7adf/wpqGnul3Xfnuooa45jda6vjYNTYfidlGcScuedyBoqO7ttv8abmj1MzQ0HYrbRXEmLTRUbbFH/iANXRDF7aI4kxazoeWFNDSF26WhC6K4XRRn0kJD1RYb1ND22zsNdY6GpkJxuyjOpIWGqi2WhuZLcbsozqTl0xvqOsevfnTUFztRQ7tX7G5eGipKcbsozqTFaGhxJK79hrp9De3VVD466ov99IYa/2fW3cDWB+8hQHGTKM6kxWroKrShy4rZwhvKg1E9iptEcSYtRzc0n5gtuaE7F/KoVIHiRlCcSUvv2HGu39Dq1TUaKnq71e8jNd92zYXdK/obmYaKUtwIijNpoaFqiw1paP/bNDRNihtBcSYtAw11axqaRkOd9W3rAxLtlqahqhQ3guJMWvxjpzz27Ia63lGaQczSaKj57aEPmVX/b0hDRSluBMWZtIxtaIYxW2RDVzRUmOJGUJxJy96GFtY0NLnbpaFpUtwIijNp8X4RyWhoeVjOXZW8FnvqhrZvIGJuihtBcSYtIxo6e1XyWiwNzZfiRlCcSUvdzX5Dh3/3PZuYLbChbl9DyejsFLeA4kxaXP2HOtc0VGOxNDRf0bbAhxcXj+5u3Lt49ueRP8pecQgNVVssDc1XpC3w6gvnOfteYaYFoaFqiz1hQ5uPsNFQDVG2wM0T13P77dwzLcpuQ0cchieuSl6LneJ2B6/Yb2iTThqqIMYWKBJ673n1FP7D60fuuIiyVxxCQ9UWG3t1Og1d0VAlMbbA1ebZ+2P/glfnzn09/ufZKw6hoWqLpaH5irAFtg9De8W8OuqBKHvFITRUbbFzNdTR0NlF2AIfH7qzH7sXvTt3n/02+gbYKw6hoWqLnauhKxo6uzgN7QfTuGgP9oo9XHlSERqqtdjoq9NtqKOhOngcqq53kLhuQ4ujqT0MaejiG1r/p9wZyu9zxMwpxr1/ufN66OaSO+N/nj3CR0NTWOysDeUP1c0qxr1/vdmsX3lvId38tLng8fD1+9gjfFUz2y9pqOBiaWi+otz7l9sN++Wzl282/njx9Nwd9TCUhnYc1Qd0GNUAABD9SURBVNDBAzKbmNFQnFice//K9TyYf6ZUHdVQxaM/i8XS0HxFuvffP3We+78qzCRr/1sCNDSFxUo2lPeaTiLevfzh9xc/XFx8++yXY0/bREN3vlsfM+vqY9VNQ6t/Sx/9WSz29KtT7gzelZzz9pcROxYmongvK84U09ENXTUNLY+mxI7+JS52/oauaOhM5r+X3a65RzoxGpr+YqUa6mjoKcW9l29e/+Xu3XvfHflsPrctv3dXdzQ0hcXS0HzFOOfIDxfflp8OfXfuSvePOX0oDe1+k4YmsFgamq+Yvy9/7Rq3xv+mZ+4N9b+qjwfn6nfj60OKhmotlobmK2JDN//rbr1cl6cP5RzMw8Y11K39D7j4DXWJHf1LXCwNzVfEhrYnDd0+p+d3PQd9akNTO/qXuFgamq94Dd2eirkO5xXnHNnDamjzX9fYaWiqR/8SF0tD8xWvof45Qzn33T7d30QyGloeSOvjjzPNo3+Ji52hoc71G1rsNDT01E7TUM7BvA8NTX+xNDRfUZ/L09BRaGj6i52locaFdkOJaUwR31O6bk9nf83fpNuDhqa/WBqarzgNde7zb5+/uaxPZ2/8pc8TzyRtZEMjHcQLixkNbT7Lsa6/pqFRxWpoqXwC/8c37pin8pk2tN7VBxu6mKN/iYs9/eo46ztrv6Gu/7h0TU1jiHKXvvnHX8rf8mw+a392xMdDaeiahqa2WJHVWdPQ04t3l/6xCWnd0Fs/Hry6J7fNTEPTX6zI6hSGGsqz+jhOcJfe/Mdxp7HPvqH+f2loGotVWp3C3oZS0ikp3pmKM8VEQ9NfrNzq0NCTUbwzFWeajNvdfwcaWn+MOrejP8nFyq1Oae39vnCvppiK4p2pONNkXPMHxFy9JzevXlV7evX1ioams1jR1Vl7z2U67zbNtfsvkeKdqTjTZLyGrnoNLXZ7GprkYkVXZ01D41O8MxVnCtbfX0c11HW/zPHoT2yxoquzpqHxKd6ZijMFc73n7vXX5W69XrePO/vRpKEJLVZ0dcq9rvy6+8nRRR1k81K8KxVnCuZ6jztp6CIXK7o6gw1dLeogm5fiXak4UzAamsViRVenfbNyREMdD06DKN5rijMFG2houx871+7mjoYmuljR1eld50BDV46QBlC8wxRnCjaqod7xQEOTXGwaqzOmoTzLP5biHaY4U7CmlFZD3W4ke7u+63179sOQxSa8On5Ddx9z0tAwineY4kzBXO9xZ7Ez72mo+mHIYhNenX5Dm9fm212Vhh5N8Q5TnCkYDc1isWmsDg2NQfEOU5wpWLeh1c5MQ5e22DRWZ938p26o/+vzTUP9p/jOeo/JvDBbiveF4kzH83fMPQ11gzu85mHIYhNeHaOhpfoFe7fb0MF3n1BRvC8UZzreyIamdhiy2IRXx2xovUPS0ECK94XiTMdpz9RIQ/NYbBqr022o9x0a+gkU7wvFmY5DQ3NbbBqrU7BegTcbWl6Zhh6ieF8oznQcGprbYhNanfENXdHQMRTvC8WZjuNq7S/QORq65MUmtDrmJ0FoaDjF+0JxpiHO/JRHs3cW/2pfvF/v7sdJHoYsNuHVGWpo8+WhhpZXQk3xvlCcaYijoSw2rdWhoRNTvC8UZxriaCiLTWt1nPXt/qluir14RUPHULwvFGcquN1gGhetvYYO7dbWDp7QYchil7Y6NDSc4n2hOFPB3p+sK+Z4GGa92NRXh4aGU7wvFGcq2PtT86/2f7I8DLNebOqrs9NQ/2tvb6/2eRrqUbwvFGcqGLuO6zTUORqa52JTX51+Q/vfbvfxsQ11nfOZLJniGirOVDB2HUdDWewCVidCQ1c0dD6KMxU6u06zPzXP3ytrGprfYlNfnQMN9V+ooqE9imuoOFOh2J+aL5qGutqq3tuyPAyzXmzqq3Ogoc0v21X7PA31KK6h4kyFYn9qvug01Nsx1zQ0v8WmvjpjGrr9V7XP01CP4hrOP9PAhq/2r/o61TN4Gspik1+d/k6889ODDXXDB8ueQ2lJFNdw/pk6L/94F5e7W30d/1XQzu5HQ7NbbOqrY12787W391dfd44D4xiioTOaf6ajGrq759HQ7Ba7sNXZ/TYNHaS4hvPP1Ows1Rf1xfVe1F7H3PNoaHaLXdjqDH97Xe/z3rHSP3jqg8X7avA4m+JwnZniOsw/U7GzNHvMqt/Q7meZ0j0eWKz87cot1rndhrrewVMfLN5XA8fZIn7fSXEd5p+p3lUONTTx44HFyt+u4GJpaI/iOpx2pp1fB17bDS3Pv1CpHoUmfzywWPHbFV5sfVAUOgdUcYEzG9r90tHQSGZqqLcrlDuBaxvqnNfQVfPPxRwPLFb0doUXu+59sq8+esqvxzTUORoaCQ3N5TBczmIXtjpjFrve+XR0c/CsaOjMpBpa7hw0lMXmtDqjFrvb0Oqy5uvBF0vrL2hoJDQ0m8NwMYtd2OqMWuyYhq5o6CzmbKhr3nPvNdR1Grq444HFat6u8mILvYY6/wf7DW1fIKu/7nxW/zTH+/QUB59ips622nud5or1HrE2G7rw44HFat6u/GJ7DTV+sDy2qv8WP9IegEZD02up4sA0NK/DcAmLXdjqjF8sDc2yofW3yuuU+8Ha+8Uj74ygrrtzLPx4YLFytyu/WOt3Tbpft0dcfWS1B+KqORRp6KSmaqi5NdpPXXQa2vmgm7Vf5HA8sFi525VfrHXF7tfruqHOb2j5xcr/ojlAE6M48FQNNd/0o6EsNqHbXcBi13ZDVzQ0oglmqrZk9e/6guorb8u59im819B59tsUjgcWm8fqTLvYLe9Nhrqh5berI5GGTipkJuMjFK75wNq6+eUJr6GutWo2b0I7JotVWuzCVifCYvvvN9TfWXfezd35BGn7nq8sxflO1FBrG6e2Y7JYkcUubHUiLHbotbL1oYbKfw5fcb4jZqoa6Vzdx+rCdkvW1/G3l7mhaSiL1bvd5Sy2/Yb5B/D2NdQ/uAUpDnZ0Q/2ttG6fpa/ay6wtObyN09kxWazIYhe2OnEXO9xQ5z11rB+frtxwQ/3PSX1adD5BtCV/eHHx6O7GvYtnfx75o6ENLTfIeveTvv3rLHLHZLFzLnZhqxN3saMbusq5oa++cJ6z72PNtNvHdhuaFy53x2Sxcy52YasTd7HWIVtc7r/vVH8Ev7yO//ZS+w5+dcX6i6MqM50oy7154npuv40yU3P7SnsIi81wsQtbnbiLHfz8tWt/unkLo/cd7yNS9XeaEhzbqYnEWG6R0HvPq6fwH14/csdF9LiGyu0hLDbDxS5sdeIudsxx22to8511/8LVIht6tXn2/ti/4NW5c1+P/3kaymJTW+zCVifuYsfceP2vfkN3LvRucqaKRljq9mFor5hXRz0QpaEsNrXFLmx1kl3s6HRMKMJCPz50Zz92L3p37j77bfQN0FAWm9piF7Y6yS52dDomFKeh/WAaF7UT7Bq9KONnAWQrPFvhFB+HAkAqYoT7cuf10M0ldyIsCABmFqOh15vH1F95byHd/LS54PHw9QEgVVFeQLjcvjLx5bOXbzb+ePH03PEwFMAyxXkR9qr/Uu+DKIsBgJlFeiPr/VO/oPd/jbMUAJhZvA8DfPj9xQ8XF98+++XY0zYBQDIUzx8KAKmgoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACEo6EAEI6GAkA4GgoA4WgoAIRLu6En+TNXAGYxd1/GSWTMAWlPH471zkqmq53Keicy5oC0pw/Hemcl09VOZb0TGXNA2tOHY72zkulqp7LeiYw5IO3pw7HeWcl0tVNZ70TGHJD29OFY76xkutqprHciYw5Ie/pwrHdWMl3tVNY7kTEHpD19ONY7K5mudirrnciYA9KePhzrnZVMVzuV9U5kzAFpTx+O9c5KpqudynonMuaAtKcPx3pnJdPVTmW9ExlzQNrTh2O9s5Lpaqey3omMOSDt6cOx3lnJdLVTWe9ExhyQ9vThWO+sZLraqax3ImMOSHv6cKx3VjJd7VTWO5ExB6Q9fTjWOyuZrnYq653ImAPSnj4c652VTFc7lfVOZMwBaU8fjvXOSqarncp6JzLmgLSnD8d6ZyXT1U5lvRMZEwAk0VAACEdDASAcDQWAcDQUAMLRUAAIR0MBIBwNBYBwNBQAwtFQAAhHQwEgHA0FgHA0FADC0VAACEdDASAcDQWAcDQUAMLRUAAIR0MBIBwNBYBwNBQAwtFQAAhHQwEgHA0FgHA0FADCLaChl+7ruUc4pdePnHP3ns89xiwy29Qb759+keXmvvl5s95n93+de44x0m/otcvpwLr5uys9eDv3KKeX16beuqq2trv129yjnNT7bxLazZNv6PV5VgfWZX1QuTtzj3JymW3qtZdQ524nEJPJfHyY0m6eekNfbY6rjA6sd5vV/ept8Wj07Me5hzmxzDb1utzaD/7cPPn4KbM13zxSuPW3dSq7edoNff+0+P+qfHavy3plr5L4f+gJZbep18VGrtb3OqsHopuHoZ+Vr11s7oHHMw9zWNINvdr8//St/8zowGp3rpsn9b/ykN2m3rpstnFem/va//8O/S2edEMv3dl3b5O4myeyeXJXP/pM4v+hp5Pdpu65zKmhrUuey0d2uX2xKKcD67oN53VmDc1tU3fl9Ti09sfTJF6xSrqhhZwOLO/B5+YhaTarXctpU3ddJxGTSRXvzZ/9de4xRqChKblqn9rQ0IxsepLAc9ppbT+UsH0BZ+45DqOhKbnsNDS3RyZZbWrf5pl8fiv+7u6Xd9P45QIamhIams2m9mwTmtEnmzw3lymseWoNrX+DoX2FPacDi+fy2a1z+XuP+iGJY/t/H/JvndLQlPCeUnbrXPx61p1ME5rGJqehKcn3s02FnDZ17Sq3X87qSuElq9QauiunA8t78HmV3zu1WW3qyvY3xr+fe4gZpfB0i4amZPMovHplLMsPXee0qUvbk28kcQ7NSXkvWV0lsMlpaFLyPefIVlabeusqz3eT2jOsbB6G6j/doqFJKc6Glum57zLb1Gv/aUdetu/G33q5PZn9eQoPFWhoWnI+B3Nmm7pzCmaX1VuIxe8oJXPuaRqaFv4WSD62D8fybGgb0QQSSkOTk/HfpMtsU3t/ESO3hpZ/ky6R3Tz9hgLAfGgoAISjoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACEo6EAEI6GAkA4GgoA4WgoAISjoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACEo6EAEI6GAkA4GgoA4WgoAISjoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACEo6EAEI6GAkA4GgoA4WgoAISjoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACEo6EAEI6GAkA4GgoA4WgoAISjoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACEo6EAEI6GAkA4GgoA4WgoAISjoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACEo6EAEI6GAkA4GgoA4WgoAISjoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACEo6EAEI6GAkA4GgoA4WgoAISjoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACEo6EAEI6GAkA4GgoA4WgoAISjoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACEo6EAEI6GAkA4GgoA4WgoAISjoQAQjoYCQDgaCgDhaCgAhKOhABCOhgJAOBoKAOFoKACE+y+hgv0wF9/KNAAAAABJRU5ErkJggg==" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNcl9tY1t3aGljaCgoTXJfbWM+eGxpbV9DRVsxXSkqKE1yX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTXI6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Mr: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNMV9tY1t3aGljaCgoTTFfbWM+eGxpbV9DRVsxXSkqKE0xX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTTE6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M1: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# Define design matrix
p_C = ncol(C)
p_C1 = sum(apply(C, 2, function(x) { all(x %in% 0:1) }))
p_C2 = p_C - p_C1
if (p_C1>0 && p_C2>0){
C1 = C[,1:p_C1]
C2 = C[,(p_C1+1):(p_C1+p_C2)]
scaC2 = apply(C2, 2, scale)
scaC = cbind(C1, scaC2)
} else if (p_C2>0){
scaC = apply(C, 2, scale)
} else {
scaC = C
}
X = cbind(Z, scaC)
matX = cbind(1, X)
matV = cbind(1, Z, V, scaC)
apply(matV[-which(is.na(V)),] %*% MCMCresult$MCMCposteriors$MbetaLists[[post_reps]], 2, mean)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDEuMDU2MjE4IDEuMjYzMTA1XG4ifQ== -->
[1] 1.056218 1.263105
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuYXBwbHkobWF0Vlstd2hpY2goaXMubmEoVikpLF0gJSolIE1DTUNyZXN1bHQkTUNNQ3Bvc3RlcmlvcnMkTWJldGFMaXN0c1tbcG9zdF9yZXBzXV0sIDIsIG1lZGlhbilcbmBgYFxuYGBgIn0= -->
```r
```r
apply(matV[-which(is.na(V)),] %*% MCMCresult$MCMCposteriors$MbetaLists[[post_reps]], 2, median)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDEuMDY0OTAwIDEuMjY5NDU0XG4ifQ== -->
[1] 1.064900 1.269454
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubl9ya1xuYGBgXG5gYGAifQ== -->
```r
```r
n_rk
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiICAgICBbLDFdIFssMl0gWywzXVxuWzEsXSAgMzU3ICAxMjggICA0OVxuWzIsXSAgIDM3ICAgNDEgICAgMFxuIn0= -->
[,1] [,2] [,3][1,] 357 128 49 [2,] 37 41 0
<!-- rnb-output-end -->
<!-- rnb-chunk-end -->
<!-- rnb-text-begin -->
\newpage
### dist. of f(M) = M
<!-- rnb-text-end -->
<!-- rnb-chunk-begin -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuc2V0LnNlZWQoMSlcbk0gPSBMSVRFZGF0YSRhdHRcblxuTUNNQ3Jlc3VsdCA9IEVEUG1lZGlhdGlvbk1DTUMoWSwgTSwgViwgWiwgQyxcbiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIGdpYmJzX2l0ZXIsIGdpYmJzX2J1cm5pbiwgZ2liYnNfdGhpbixcbiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIEQsIG51bV9NQywgbnVtX01DX3ByaW9yKVxuYGBgXG5gYGAifQ== -->
```r
```r
set.seed(1)
M = LITEdata$att
MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
gibbs_iter, gibbs_burnin, gibbs_thin,
D, num_MC, num_MC_prior)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Bur-In End 5000 Time: Tue Feb 21 18:18:33 2023 Gibbs Iteration 250 ( 5 %) Time: Tue Feb 21 18:18:39 2023 Gibbs Iteration 500 ( 10 %) Time: Tue Feb 21 18:18:47 2023 Gibbs Iteration 750 ( 15 %) Time: Tue Feb 21 18:18:54 2023 Gibbs Iteration 1000 ( 20 %) Time: Tue Feb 21 18:19:00 2023 Gibbs Iteration 1250 ( 25 %) Time: Tue Feb 21 18:19:08 2023 Gibbs Iteration 1500 ( 30 %) Time: Tue Feb 21 18:19:16 2023 Gibbs Iteration 1750 ( 35 %) Time: Tue Feb 21 18:19:24 2023 Gibbs Iteration 2000 ( 40 %) Time: Tue Feb 21 18:19:32 2023 Gibbs Iteration 2250 ( 45 %) Time: Tue Feb 21 18:19:39 2023 Gibbs Iteration 2500 ( 50 %) Time: Tue Feb 21 18:19:47 2023 Gibbs Iteration 2750 ( 55 %) Time: Tue Feb 21 18:19:55 2023 Gibbs Iteration 3000 ( 60 %) Time: Tue Feb 21 18:20:03 2023 Gibbs Iteration 3250 ( 65 %) Time: Tue Feb 21 18:20:10 2023 Gibbs Iteration 3500 ( 70 %) Time: Tue Feb 21 18:20:18 2023 Gibbs Iteration 3750 ( 75 %) Time: Tue Feb 21 18:20:26 2023 Gibbs Iteration 4000 ( 80 %) Time: Tue Feb 21 18:20:34 2023 Gibbs Iteration 4250 ( 85 %) Time: Tue Feb 21 18:20:42 2023 Gibbs Iteration 4500 ( 90 %) Time: Tue Feb 21 18:20:49 2023 Gibbs Iteration 4750 ( 95 %) Time: Tue Feb 21 18:20:57 2023 Gibbs Iteration 5000 ( 100 %) Time: Tue Feb 21 18:21:04 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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-->
```r
```r
{
# Significance Level alpha
level = 0.05
quantile_alpha = c(level/2,1-level/2)
# the number of Gibbs Sampler stored
n_MCMC = MCMCresult$constants$n_MCMC
# Define interation check
iter_check = floor(n_MCMC/10)
M0_mc = list(NA)
Mr_mc = list(NA)
M1_mc = list(NA)
N = MCMCresult$constants$N
D = MCMCresult$constants$D
num_MC = MCMCresult$constants$num_MC
p_V = MCMCresult$constants$p_V
p_Z = MCMCresult$constants$p_Z
p_C1 = MCMCresult$constants$p_C1
p_C2 = MCMCresult$constants$p_C2
f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
a_Ysig2 = MCMCresult$priors$a_Ysig2
b_Ysig2 = MCMCresult$priors$b_Ysig2
a_Ybeta = MCMCresult$priors$a_Ybeta
B_Ybeta = MCMCresult$priors$B_Ybeta
a_Msig2 = MCMCresult$priors$a_Msig2
b_Msig2 = MCMCresult$priors$b_Msig2
a_Mbeta = MCMCresult$priors$a_Mbeta
B_Mbeta = MCMCresult$priors$B_Mbeta
a_Vsig2 = MCMCresult$priors$a_Vsig2
b_Vsig2 = MCMCresult$priors$b_Vsig2
a_Vbeta = MCMCresult$priors$a_Vbeta
B_Vbeta = MCMCresult$priors$B_Vbeta
a_pi = MCMCresult$priors$a_pi
b_pi = MCMCresult$priors$b_pi
a_mu = MCMCresult$priors$a_mu
b_mu = MCMCresult$priors$b_mu
a_tau2 = MCMCresult$priors$a_tau2
b_tau2 = MCMCresult$priors$b_tau2
alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
rho = runif(n_MCMC)
# End initial values ------------------------------------------------------------
for (post_reps in 1:n_MCMC) {
Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
rho_mc = rho[post_reps] * rep(1,D)
YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
ZpiPars_array = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
XpiPars_array = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
XmuPars_array = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
alpha_theta = alpha_theta_draws[post_reps]
alpha_omega = alpha_omega_draws[post_reps]
MCresult = EDPpostmc_concon(p_C1, p_C2,
n_k, n_rk, Ky, Kyx, max_Kx_Sy,
D, num_MC, rho_mc,
YbetaPars, Ysig2Pars,
MbetaPars, Msig2Pars,
VbetaPars_array, Vsig2Pars_array,
ZpiPars_array, XpiPars_array,
XmuPars_array, Xtau2Pars_array,
alpha_theta, alpha_omega,
f0_z0_mc, f0_z1_mc,
YbetaPrior_mc,
MbetaPrior_mc, Msig2Prior_mc,
VbetaPrior_mc, Vsig2Prior_mc,
a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
M0_mc[[post_reps]] = MCresult$M0_mc
Mr_mc[[post_reps]] = MCresult$Mr_mc
M1_mc[[post_reps]] = MCresult$M1_mc
if (post_reps %% iter_check == 0){
cat(\Post-Processing\,post_reps,\(\,(post_reps/n_MCMC)*100,\%)\,\Time:\,date(),\\n\)
}
}
distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:21:05 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:21:06 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:21:06 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:21:07 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:21:07 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:21:08 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:21:08 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:21:09 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:21:09 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:21:09 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTTBfbWMgPSB1bmxpc3QoZGlzdE0kTTBfbWMpXG5Ncl9tYyA9IHVubGlzdChkaXN0TSRNcl9tYylcbk0xX21jID0gdW5saXN0KGRpc3RNJE0xX21jKVxuXG5tZWFuKE0pXG5gYGBcbmBgYCJ9 -->
```r
```r
M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)
mean(M)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuNTMwOTNcbiJ9 -->
[1] 0.53093
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTBdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==0])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuNTI0MDUzNlxuIn0= -->
[1] 0.5240536
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTFdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==1])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuNTM4MzE5MlxuIn0= -->
[1] 0.5383192
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)
# print(\dist. of M based on the data\)
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Data\,col=\green\)
legend(\topright\, legend=c(\M\, \M[Z==0]\, \M[Z==1]\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# print(\dist. of M based on the G-computation\)
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\G-computation\,col=\green\)
abline(v = 0, col = \black\, lwd = 2)abline(v = 1, col = \black\, lwd = 2)
legend(\topright\, legend=c(\M0\, \Mr\, \M1\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDEwMClcbmhpc3QoTSx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE06IGRhdGFcXClcbmBgYFxuYGBgIn0= -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTBdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0wXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==0]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTFdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0xXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==1]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDM1MClcbmhpc3QoTTBfbWNbd2hpY2goKE0wX21jPnhsaW1fQ0VbMV0pKihNMF9tYzx4bGltX0NFWzJdKT09MSldLDFlMyx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE0wOiBHLWNvbXB1dGF0aW9uXFwpXG5gYGBcbmBgYCJ9 -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M0: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNcl9tY1t3aGljaCgoTXJfbWM+eGxpbV9DRVsxXSkqKE1yX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTXI6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Mr: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNMV9tY1t3aGljaCgoTTFfbWM+eGxpbV9DRVsxXSkqKE0xX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTTE6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M1: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIC0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS1cbiMgLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLVxuIyAtLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tXG5yaG8gPSBcXHVuaWZcXFxuUE9TVHJlc3VsdFJob1VuaWYgPSBFRFBtZWRpYXRpb25QT1NUKE1DTUNyZXN1bHQsIGVzdHR5cGUsIHJobywgc2F2ZV9jbHVzdGVyKVxuYGBgXG5gYGAifQ== -->
```r
```r
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = \unif\
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:21:14 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:21:14 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:21:15 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:21:15 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:21:15 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:21:16 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:21:16 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:21:17 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:21:17 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:21:18 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc
CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c(\NIE\,\NDE\,\ATE\)
NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE
q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col=\red\,ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col=\blue\,ylim=ylim_CE);par(new=T)plot(sort(ATErhoUnif),col=\green\,ylim=ylim_CE)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuQ0VfdGFibGVSaG9VbmlmXG5gYGBcbmBgYCJ9 -->
```r
```r
CE_tableRhoUnif
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiICAgICAgZXN0aW1hdGVzICAgICAgICBzZCBxdWFudGlsZTAyNSBxdWFudGlsZTk3NSBDSWxlbmd0aDk1XG5OSUUgLTAuMDYyMzMzOTYgMC4xNjkxNjUxICAtMC4zNjc2NTQ0ICAgMC4yNzUzMzc2ICAgMC42NDI5OTJcbk5ERSAtMy4wMDIwMzk0NSAwLjkyODkxODggIC00LjM0MDEyNzYgIC0xLjUzMjM2NDUgICAyLjgwNzc2M1xuQVRFIC0zLjA2NDM3MzQxIDAuOTM4NTk3OCAgLTQuNjUyMTk4OCAgLTEuNTc2MDE0MCAgIDMuMDc2MTg1XG4ifQ== -->
estimates sd quantile025 quantile975 CIlength95NIE -0.06233396 0.1691651 -0.3676544 0.2753376 0.642992 NDE -3.00203945 0.9289188 -4.3401276 -1.5323645 2.807763 ATE -3.06437341 0.9385978 -4.6521988 -1.5760140 3.076185
<!-- rnb-output-end -->
<!-- rnb-chunk-end -->
<!-- rnb-text-begin -->
\newpage
### dist. of f(M) = scale(M)
<!-- rnb-text-end -->
<!-- rnb-chunk-begin -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuc2V0LnNlZWQoMSlcbk0gPSBMSVRFZGF0YSRhdHRcbk0gPSBhcy5udW1lcmljKHNjYWxlKE0pKVxuXG5NQ01DcmVzdWx0ID0gRURQbWVkaWF0aW9uTUNNQyhZLCBNLCBWLCBaLCBDLFxuICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgZ2liYnNfaXRlciwgZ2liYnNfYnVybmluLCBnaWJic190aGluLFxuICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgRCwgbnVtX01DLCBudW1fTUNfcHJpb3IpXG5gYGBcbmBgYCJ9 -->
```r
```r
set.seed(1)
M = LITEdata$att
M = as.numeric(scale(M))
MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
gibbs_iter, gibbs_burnin, gibbs_thin,
D, num_MC, num_MC_prior)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Bur-In End 5000 Time: Tue Feb 21 18:24:20 2023 Gibbs Iteration 250 ( 5 %) Time: Tue Feb 21 18:24:27 2023 Gibbs Iteration 500 ( 10 %) Time: Tue Feb 21 18:24:37 2023 Gibbs Iteration 750 ( 15 %) Time: Tue Feb 21 18:24:45 2023 Gibbs Iteration 1000 ( 20 %) Time: Tue Feb 21 18:24:53 2023 Gibbs Iteration 1250 ( 25 %) Time: Tue Feb 21 18:25:02 2023 Gibbs Iteration 1500 ( 30 %) Time: Tue Feb 21 18:25:10 2023 Gibbs Iteration 1750 ( 35 %) Time: Tue Feb 21 18:25:19 2023 Gibbs Iteration 2000 ( 40 %) Time: Tue Feb 21 18:25:27 2023 Gibbs Iteration 2250 ( 45 %) Time: Tue Feb 21 18:25:36 2023 Gibbs Iteration 2500 ( 50 %) Time: Tue Feb 21 18:25:44 2023 Gibbs Iteration 2750 ( 55 %) Time: Tue Feb 21 18:25:52 2023 Gibbs Iteration 3000 ( 60 %) Time: Tue Feb 21 18:26:00 2023 Gibbs Iteration 3250 ( 65 %) Time: Tue Feb 21 18:26:07 2023 Gibbs Iteration 3500 ( 70 %) Time: Tue Feb 21 18:26:15 2023 Gibbs Iteration 3750 ( 75 %) Time: Tue Feb 21 18:26:22 2023 Gibbs Iteration 4000 ( 80 %) Time: Tue Feb 21 18:26:30 2023 Gibbs Iteration 4250 ( 85 %) Time: Tue Feb 21 18:26:38 2023 Gibbs Iteration 4500 ( 90 %) Time: Tue Feb 21 18:26:45 2023 Gibbs Iteration 4750 ( 95 %) Time: Tue Feb 21 18:26:53 2023 Gibbs Iteration 5000 ( 100 %) Time: Tue Feb 21 18:27:01 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxue1xuICAjIFNpZ25pZmljYW5jZSBMZXZlbCBhbHBoYVxuICBsZXZlbCA9IDAuMDVcbiAgcXVhbnRpbGVfYWxwaGEgPSBjKGxldmVsLzIsMS1sZXZlbC8yKVxuICBcbiAgIyB0aGUgbnVtYmVyIG9mIEdpYmJzIFNhbXBsZXIgc3RvcmVkXG4gIG5fTUNNQyA9IE1DTUNyZXN1bHQkY29uc3RhbnRzJG5fTUNNQ1xuICBcbiAgIyBEZWZpbmUgaW50ZXJhdGlvbiBjaGVja1xuICBpdGVyX2NoZWNrID0gZmxvb3Iobl9NQ01DLzEwKVxuICBcbiAgTTBfbWMgPSBsaXN0KE5BKVxuICBNcl9tYyA9IGxpc3QoTkEpXG4gIE0xX21jID0gbGlzdChOQSlcbiAgXG4gIE4gPSBNQ01DcmVzdWx0JGNvbnN0YW50cyROXG4gIEQgPSBNQ01DcmVzdWx0JGNvbnN0YW50cyREXG4gIG51bV9NQyA9IE1DTUNyZXN1bHQkY29uc3RhbnRzJG51bV9NQ1xuICBwX1YgPSBNQ01DcmVzdWx0JGNvbnN0YW50cyRwX1ZcbiAgcF9aID0gTUNNQ3Jlc3VsdCRjb25zdGFudHMkcF9aXG4gIHBfQzEgPSBNQ01DcmVzdWx0JGNvbnN0YW50cyRwX0MxXG4gIHBfQzIgPSBNQ01DcmVzdWx0JGNvbnN0YW50cyRwX0MyXG4gIFxuICBmMF96MF9tYyA9IE1DTUNyZXN1bHQkTUNwcmlvcnMkZjBfejBfbWNcbiAgZjBfejFfbWMgPSBNQ01DcmVzdWx0JE1DcHJpb3JzJGYwX3oxX21jXG4gIFliZXRhUHJpb3JfbWMgPSBNQ01DcmVzdWx0JE1DcHJpb3JzJFliZXRhUHJpb3JfbWNcbiAgTWJldGFQcmlvcl9tYyA9IE1DTUNyZXN1bHQkTUNwcmlvcnMkTWJldGFQcmlvcl9tY1xuICBNc2lnMlByaW9yX21jID0gTUNNQ3Jlc3VsdCRNQ3ByaW9ycyRNc2lnMlByaW9yX21jXG4gIFZiZXRhUHJpb3JfbWMgPSBNQ01DcmVzdWx0JE1DcHJpb3JzJFZiZXRhUHJpb3JfbWNcbiAgVnNpZzJQcmlvcl9tYyA9IE1DTUNyZXN1bHQkTUNwcmlvcnMkVnNpZzJQcmlvcl9tY1xuICBcbiAgYV9Zc2lnMiA9IE1DTUNyZXN1bHQkcHJpb3JzJGFfWXNpZzJcbiAgYl9Zc2lnMiA9IE1DTUNyZXN1bHQkcHJpb3JzJGJfWXNpZzJcbiAgYV9ZYmV0YSA9IE1DTUNyZXN1bHQkcHJpb3JzJGFfWWJldGFcbiAgQl9ZYmV0YSA9IE1DTUNyZXN1bHQkcHJpb3JzJEJfWWJldGFcbiAgYV9Nc2lnMiA9IE1DTUNyZXN1bHQkcHJpb3JzJGFfTXNpZzJcbiAgYl9Nc2lnMiA9IE1DTUNyZXN1bHQkcHJpb3JzJGJfTXNpZzJcbiAgYV9NYmV0YSA9IE1DTUNyZXN1bHQkcHJpb3JzJGFfTWJldGFcbiAgQl9NYmV0YSA9IE1DTUNyZXN1bHQkcHJpb3JzJEJfTWJldGFcbiAgYV9Wc2lnMiA9IE1DTUNyZXN1bHQkcHJpb3JzJGFfVnNpZzJcbiAgYl9Wc2lnMiA9IE1DTUNyZXN1bHQkcHJpb3JzJGJfVnNpZzJcbiAgYV9WYmV0YSA9IE1DTUNyZXN1bHQkcHJpb3JzJGFfVmJldGFcbiAgQl9WYmV0YSA9IE1DTUNyZXN1bHQkcHJpb3JzJEJfVmJldGFcbiAgYV9waSAgID0gTUNNQ3Jlc3VsdCRwcmlvcnMkYV9waVxuICBiX3BpICAgPSBNQ01DcmVzdWx0JHByaW9ycyRiX3BpXG4gIGFfbXUgICA9IE1DTUNyZXN1bHQkcHJpb3JzJGFfbXVcbiAgYl9tdSAgID0gTUNNQ3Jlc3VsdCRwcmlvcnMkYl9tdVxuICBhX3RhdTIgPSBNQ01DcmVzdWx0JHByaW9ycyRhX3RhdTJcbiAgYl90YXUyID0gTUNNQ3Jlc3VsdCRwcmlvcnMkYl90YXUyXG4gIFxuICBhbHBoYV90aGV0YV9kcmF3cyA9IE1DTUNyZXN1bHQkTUNNQ3Bvc3RlcmlvcnMkYWxwaGFfdGhldGFfZHJhd3NcbiAgYWxwaGFfb21lZ2FfZHJhd3MgPSBNQ01DcmVzdWx0JE1DTUNwb3N0ZXJpb3JzJGFscGhhX29tZWdhX2RyYXdzXG4gIFxuICByaG8gPSBydW5pZihuX01DTUMpXG4gIFxuICAjIEVuZCBpbml0aWFsIHZhbHVlcyAtLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS1cbiAgZm9yIChwb3N0X3JlcHMgaW4gMTpuX01DTUMpIHtcbiAgICBLeSA9IE1DTUNyZXN1bHQkTUNNQ3Bvc3RlcmlvcnMkS3lMaXN0c1tbcG9zdF9yZXBzXV1cbiAgICBLeXggPSBNQ01DcmVzdWx0JE1DTUNwb3N0ZXJpb3JzJEt5eExpc3RzW1twb3N0X3JlcHNdXVxuICAgIG5fayA9IE1DTUNyZXN1bHQkTUNNQ3Bvc3RlcmlvcnMkbl9rTGlzdHNbW3Bvc3RfcmVwc11dXG4gICAgbl9yayA9IE1DTUNyZXN1bHQkTUNNQ3Bvc3RlcmlvcnMkbl9ya0xpc3RzW1twb3N0X3JlcHNdXVxuICAgIG1heF9LeF9TeSA9IE1DTUNyZXN1bHQkTUNNQ3Bvc3RlcmlvcnMkbWF4X0t4X1N5TGlzdHNbW3Bvc3RfcmVwc11dXG4gICAgXG4gICAgcmhvX21jID0gcmhvW3Bvc3RfcmVwc10gKiByZXAoMSxEKVxuICAgIFliZXRhUGFycyA9IE1DTUNyZXN1bHQkTUNNQ3Bvc3RlcmlvcnMkWWJldGFMaXN0c1tbcG9zdF9yZXBzXV1cbiAgICBZc2lnMlBhcnMgPSBNQ01DcmVzdWx0JE1DTUNwb3N0ZXJpb3JzJFlzaWcyTGlzdHNbW3Bvc3RfcmVwc11dXG4gICAgTWJldGFQYXJzID0gTUNNQ3Jlc3VsdCRNQ01DcG9zdGVyaW9ycyRNYmV0YUxpc3RzW1twb3N0X3JlcHNdXVxuICAgIE1zaWcyUGFycyA9IE1DTUNyZXN1bHQkTUNNQ3Bvc3RlcmlvcnMkTXNpZzJMaXN0c1tbcG9zdF9yZXBzXV1cbiAgICBWYmV0YVBhcnNfYXJyYXkgPSBNQ01DcmVzdWx0JE1DTUNwb3N0ZXJpb3JzJFZiZXRhTGlzdHNbW3Bvc3RfcmVwc11dXG4gICAgVnNpZzJQYXJzX2FycmF5ID0gTUNNQ3Jlc3VsdCRNQ01DcG9zdGVyaW9ycyRWc2lnMkxpc3RzW1twb3N0X3JlcHNdXVxuICAgIFpwaVBhcnNfYXJyYXkgICA9IE1DTUNyZXN1bHQkTUNNQ3Bvc3RlcmlvcnMkWnBpTGlzdHNbW3Bvc3RfcmVwc11dXG4gICAgWHBpUGFyc19hcnJheSAgID0gTUNNQ3Jlc3VsdCRNQ01DcG9zdGVyaW9ycyRYcGlMaXN0c1tbcG9zdF9yZXBzXV1cbiAgICBYbXVQYXJzX2FycmF5ICAgPSBNQ01DcmVzdWx0JE1DTUNwb3N0ZXJpb3JzJFhtdUxpc3RzW1twb3N0X3JlcHNdXVxuICAgIFh0YXUyUGFyc19hcnJheSA9IE1DTUNyZXN1bHQkTUNNQ3Bvc3RlcmlvcnMkWHRhdTJMaXN0c1tbcG9zdF9yZXBzXV1cbiAgICBhbHBoYV90aGV0YSA9IGFscGhhX3RoZXRhX2RyYXdzW3Bvc3RfcmVwc11cbiAgICBhbHBoYV9vbWVnYSA9IGFscGhhX29tZWdhX2RyYXdzW3Bvc3RfcmVwc11cbiAgICBcbiAgICBNQ3Jlc3VsdCA9IEVEUHBvc3RtY19jb25jb24ocF9DMSwgcF9DMixcbiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgbl9rLCBuX3JrLCBLeSwgS3l4LCBtYXhfS3hfU3ksIFxuICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICBELCBudW1fTUMsIHJob19tYyxcbiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgWWJldGFQYXJzLCBZc2lnMlBhcnMsXG4gICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIE1iZXRhUGFycywgTXNpZzJQYXJzLFxuICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICBWYmV0YVBhcnNfYXJyYXksIFZzaWcyUGFyc19hcnJheSxcbiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgWnBpUGFyc19hcnJheSwgWHBpUGFyc19hcnJheSwgXG4gICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIFhtdVBhcnNfYXJyYXksIFh0YXUyUGFyc19hcnJheSxcbiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgYWxwaGFfdGhldGEsIGFscGhhX29tZWdhLCBcbiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgZjBfejBfbWMsIGYwX3oxX21jLFxuICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICBZYmV0YVByaW9yX21jLCBcbiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgTWJldGFQcmlvcl9tYywgTXNpZzJQcmlvcl9tYyxcbiAgICAg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-->
```r
```r
{
# Significance Level alpha
level = 0.05
quantile_alpha = c(level/2,1-level/2)
# the number of Gibbs Sampler stored
n_MCMC = MCMCresult$constants$n_MCMC
# Define interation check
iter_check = floor(n_MCMC/10)
M0_mc = list(NA)
Mr_mc = list(NA)
M1_mc = list(NA)
N = MCMCresult$constants$N
D = MCMCresult$constants$D
num_MC = MCMCresult$constants$num_MC
p_V = MCMCresult$constants$p_V
p_Z = MCMCresult$constants$p_Z
p_C1 = MCMCresult$constants$p_C1
p_C2 = MCMCresult$constants$p_C2
f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
a_Ysig2 = MCMCresult$priors$a_Ysig2
b_Ysig2 = MCMCresult$priors$b_Ysig2
a_Ybeta = MCMCresult$priors$a_Ybeta
B_Ybeta = MCMCresult$priors$B_Ybeta
a_Msig2 = MCMCresult$priors$a_Msig2
b_Msig2 = MCMCresult$priors$b_Msig2
a_Mbeta = MCMCresult$priors$a_Mbeta
B_Mbeta = MCMCresult$priors$B_Mbeta
a_Vsig2 = MCMCresult$priors$a_Vsig2
b_Vsig2 = MCMCresult$priors$b_Vsig2
a_Vbeta = MCMCresult$priors$a_Vbeta
B_Vbeta = MCMCresult$priors$B_Vbeta
a_pi = MCMCresult$priors$a_pi
b_pi = MCMCresult$priors$b_pi
a_mu = MCMCresult$priors$a_mu
b_mu = MCMCresult$priors$b_mu
a_tau2 = MCMCresult$priors$a_tau2
b_tau2 = MCMCresult$priors$b_tau2
alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
rho = runif(n_MCMC)
# End initial values ------------------------------------------------------------
for (post_reps in 1:n_MCMC) {
Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
rho_mc = rho[post_reps] * rep(1,D)
YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
ZpiPars_array = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
XpiPars_array = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
XmuPars_array = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
alpha_theta = alpha_theta_draws[post_reps]
alpha_omega = alpha_omega_draws[post_reps]
MCresult = EDPpostmc_concon(p_C1, p_C2,
n_k, n_rk, Ky, Kyx, max_Kx_Sy,
D, num_MC, rho_mc,
YbetaPars, Ysig2Pars,
MbetaPars, Msig2Pars,
VbetaPars_array, Vsig2Pars_array,
ZpiPars_array, XpiPars_array,
XmuPars_array, Xtau2Pars_array,
alpha_theta, alpha_omega,
f0_z0_mc, f0_z1_mc,
YbetaPrior_mc,
MbetaPrior_mc, Msig2Prior_mc,
VbetaPrior_mc, Vsig2Prior_mc,
a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
M0_mc[[post_reps]] = MCresult$M0_mc
Mr_mc[[post_reps]] = MCresult$Mr_mc
M1_mc[[post_reps]] = MCresult$M1_mc
if (post_reps %% iter_check == 0){
cat(\Post-Processing\,post_reps,\(\,(post_reps/n_MCMC)*100,\%)\,\Time:\,date(),\\n\)
}
}
distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:27:02 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:27:03 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:27:03 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:27:03 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:27:04 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:27:04 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:27:05 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:27:05 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:27:06 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:27:06 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTTBfbWMgPSB1bmxpc3QoZGlzdE0kTTBfbWMpXG5Ncl9tYyA9IHVubGlzdChkaXN0TSRNcl9tYylcbk0xX21jID0gdW5saXN0KGRpc3RNJE0xX21jKVxuXG5tZWFuKE0pXG5gYGBcbmBgYCJ9 -->
```r
```r
M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)
mean(M)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIC00Ljc1NjMxN2UtMTdcbiJ9 -->
[1] -4.756317e-17
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTBdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==0])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIC0wLjAxOTg4NDE0XG4ifQ== -->
[1] -0.01988414
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTFdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==1])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuMDIxMzY3MDNcbiJ9 -->
[1] 0.02136703
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)
# print(\dist. of M based on the data\)
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Data\,col=\green\)
legend(\topright\, legend=c(\M\, \M[Z==0]\, \M[Z==1]\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# print(\dist. of M based on the G-computation\)
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\G-computation\,col=\green\)
abline(v = 0, col = \black\, lwd = 2)abline(v = 1, col = \black\, lwd = 2)
legend(\topright\, legend=c(\M0\, \Mr\, \M1\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDEwMClcbmhpc3QoTSx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE06IGRhdGFcXClcbmBgYFxuYGBgIn0= -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTBdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0wXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==0]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTFdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0xXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==1]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDM1MClcbmhpc3QoTTBfbWNbd2hpY2goKE0wX21jPnhsaW1fQ0VbMV0pKihNMF9tYzx4bGltX0NFWzJdKT09MSldLDFlMyx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE0wOiBHLWNvbXB1dGF0aW9uXFwpXG5gYGBcbmBgYCJ9 -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M0: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNcl9tY1t3aGljaCgoTXJfbWM+eGxpbV9DRVsxXSkqKE1yX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTXI6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Mr: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNMV9tY1t3aGljaCgoTTFfbWM+eGxpbV9DRVsxXSkqKE0xX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTTE6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M1: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIC0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS1cbiMgLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLVxuIyAtLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tXG5yaG8gPSBcXHVuaWZcXFxuUE9TVHJlc3VsdFJob1VuaWYgPSBFRFBtZWRpYXRpb25QT1NUKE1DTUNyZXN1bHQsIGVzdHR5cGUsIHJobywgc2F2ZV9jbHVzdGVyKVxuYGBgXG5gYGAifQ== -->
```r
```r
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = \unif\
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:27:10 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:27:11 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:27:11 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:27:12 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:27:12 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:27:13 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:27:13 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:27:13 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:27:14 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:27:14 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc
CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c(\NIE\,\NDE\,\ATE\)
NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE
q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col=\red\,ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col=\blue\,ylim=ylim_CE);par(new=T)plot(sort(ATErhoUnif),col=\green\,ylim=ylim_CE)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuQ0VfdGFibGVSaG9VbmlmXG5gYGBcbmBgYCJ9 -->
```r
```r
CE_tableRhoUnif
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiICAgICAgZXN0aW1hdGVzICAgICAgICBzZCBxdWFudGlsZTAyNSBxdWFudGlsZTk3NSBDSWxlbmd0aDk1XG5OSUUgLTAuMDUwNzkyNjEgMC4xMDg3OTM1ICAtMC4yNTA1MzMzICAgMC4xNTI3MDY2ICAwLjQwMzIzOTlcbk5ERSAtMi45MTE5NDY3NiAxLjAxNTcxMTYgIC00LjIzNDM5OTQgIC0xLjI5NTEyOTQgIDIuOTM5MjcwMFxuQVRFIC0yLjk2MjczOTM4IDEuMDIwNzgxNyAgLTQuMzQxNjk3NCAgLTEuMzU4NzUxMSAgMi45ODI5NDYzXG4ifQ== -->
estimates sd quantile025 quantile975 CIlength95NIE -0.05079261 0.1087935 -0.2505333 0.1527066 0.4032399 NDE -2.91194676 1.0157116 -4.2343994 -1.2951294 2.9392700 ATE -2.96273938 1.0207817 -4.3416974 -1.3587511 2.9829463
<!-- rnb-output-end -->
<!-- rnb-chunk-end -->
<!-- rnb-text-begin -->
\newpage
### dist. of f(M) = exp(M)
<!-- rnb-text-end -->
<!-- rnb-chunk-begin -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuc2V0LnNlZWQoMSlcbk0gPSBMSVRFZGF0YSRhdHRcbk0gPSBleHAoTSlcblxuTUNNQ3Jlc3VsdCA9IEVEUG1lZGlhdGlvbk1DTUMoWSwgTSwgViwgWiwgQyxcbiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIGdpYmJzX2l0ZXIsIGdpYmJzX2J1cm5pbiwgZ2liYnNfdGhpbixcbiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIEQsIG51bV9NQywgbnVtX01DX3ByaW9yKVxuYGBgXG5gYGAifQ== -->
```r
```r
set.seed(1)
M = LITEdata$att
M = exp(M)
MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
gibbs_iter, gibbs_burnin, gibbs_thin,
D, num_MC, num_MC_prior)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Bur-In End 5000 Time: Tue Feb 21 18:30:15 2023 Gibbs Iteration 250 ( 5 %) Time: Tue Feb 21 18:30:22 2023 Gibbs Iteration 500 ( 10 %) Time: Tue Feb 21 18:30:29 2023 Gibbs Iteration 750 ( 15 %) Time: Tue Feb 21 18:30:36 2023 Gibbs Iteration 1000 ( 20 %) Time: Tue Feb 21 18:30:43 2023 Gibbs Iteration 1250 ( 25 %) Time: Tue Feb 21 18:30:51 2023 Gibbs Iteration 1500 ( 30 %) Time: Tue Feb 21 18:30:58 2023 Gibbs Iteration 1750 ( 35 %) Time: Tue Feb 21 18:31:05 2023 Gibbs Iteration 2000 ( 40 %) Time: Tue Feb 21 18:31:12 2023 Gibbs Iteration 2250 ( 45 %) Time: Tue Feb 21 18:31:19 2023 Gibbs Iteration 2500 ( 50 %) Time: Tue Feb 21 18:31:26 2023 Gibbs Iteration 2750 ( 55 %) Time: Tue Feb 21 18:31:33 2023 Gibbs Iteration 3000 ( 60 %) Time: Tue Feb 21 18:31:41 2023 Gibbs Iteration 3250 ( 65 %) Time: Tue Feb 21 18:31:48 2023 Gibbs Iteration 3500 ( 70 %) Time: Tue Feb 21 18:31:55 2023 Gibbs Iteration 3750 ( 75 %) Time: Tue Feb 21 18:32:02 2023 Gibbs Iteration 4000 ( 80 %) Time: Tue Feb 21 18:32:09 2023 Gibbs Iteration 4250 ( 85 %) Time: Tue Feb 21 18:32:16 2023 Gibbs Iteration 4500 ( 90 %) Time: Tue Feb 21 18:32:23 2023 Gibbs Iteration 4750 ( 95 %) Time: Tue Feb 21 18:32:31 2023 Gibbs Iteration 5000 ( 100 %) Time: Tue Feb 21 18:32:39 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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-->
```r
```r
{
# Significance Level alpha
level = 0.05
quantile_alpha = c(level/2,1-level/2)
# the number of Gibbs Sampler stored
n_MCMC = MCMCresult$constants$n_MCMC
# Define interation check
iter_check = floor(n_MCMC/10)
M0_mc = list(NA)
Mr_mc = list(NA)
M1_mc = list(NA)
N = MCMCresult$constants$N
D = MCMCresult$constants$D
num_MC = MCMCresult$constants$num_MC
p_V = MCMCresult$constants$p_V
p_Z = MCMCresult$constants$p_Z
p_C1 = MCMCresult$constants$p_C1
p_C2 = MCMCresult$constants$p_C2
f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
a_Ysig2 = MCMCresult$priors$a_Ysig2
b_Ysig2 = MCMCresult$priors$b_Ysig2
a_Ybeta = MCMCresult$priors$a_Ybeta
B_Ybeta = MCMCresult$priors$B_Ybeta
a_Msig2 = MCMCresult$priors$a_Msig2
b_Msig2 = MCMCresult$priors$b_Msig2
a_Mbeta = MCMCresult$priors$a_Mbeta
B_Mbeta = MCMCresult$priors$B_Mbeta
a_Vsig2 = MCMCresult$priors$a_Vsig2
b_Vsig2 = MCMCresult$priors$b_Vsig2
a_Vbeta = MCMCresult$priors$a_Vbeta
B_Vbeta = MCMCresult$priors$B_Vbeta
a_pi = MCMCresult$priors$a_pi
b_pi = MCMCresult$priors$b_pi
a_mu = MCMCresult$priors$a_mu
b_mu = MCMCresult$priors$b_mu
a_tau2 = MCMCresult$priors$a_tau2
b_tau2 = MCMCresult$priors$b_tau2
alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
rho = runif(n_MCMC)
# End initial values ------------------------------------------------------------
for (post_reps in 1:n_MCMC) {
Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
rho_mc = rho[post_reps] * rep(1,D)
YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
ZpiPars_array = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
XpiPars_array = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
XmuPars_array = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
alpha_theta = alpha_theta_draws[post_reps]
alpha_omega = alpha_omega_draws[post_reps]
MCresult = EDPpostmc_concon(p_C1, p_C2,
n_k, n_rk, Ky, Kyx, max_Kx_Sy,
D, num_MC, rho_mc,
YbetaPars, Ysig2Pars,
MbetaPars, Msig2Pars,
VbetaPars_array, Vsig2Pars_array,
ZpiPars_array, XpiPars_array,
XmuPars_array, Xtau2Pars_array,
alpha_theta, alpha_omega,
f0_z0_mc, f0_z1_mc,
YbetaPrior_mc,
MbetaPrior_mc, Msig2Prior_mc,
VbetaPrior_mc, Vsig2Prior_mc,
a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
M0_mc[[post_reps]] = MCresult$M0_mc
Mr_mc[[post_reps]] = MCresult$Mr_mc
M1_mc[[post_reps]] = MCresult$M1_mc
if (post_reps %% iter_check == 0){
cat(\Post-Processing\,post_reps,\(\,(post_reps/n_MCMC)*100,\%)\,\Time:\,date(),\\n\)
}
}
distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:32:40 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:32:40 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:32:41 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:32:41 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:32:41 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:32:42 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:32:42 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:32:43 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:32:43 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:32:44 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTTBfbWMgPSB1bmxpc3QoZGlzdE0kTTBfbWMpXG5Ncl9tYyA9IHVubGlzdChkaXN0TSRNcl9tYylcbk0xX21jID0gdW5saXN0KGRpc3RNJE0xX21jKVxuXG5tZWFuKE0pXG5gYGBcbmBgYCJ9 -->
```r
```r
M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)
mean(M)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDEuODAxMDY3XG4ifQ== -->
[1] 1.801067
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTBdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==0])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDEuODA1NDcxXG4ifQ== -->
[1] 1.805471
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTFdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==1])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDEuNzk2MzM1XG4ifQ== -->
[1] 1.796335
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)
# print(\dist. of M based on the data\)
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Data\,col=\green\)
legend(\topright\, legend=c(\M\, \M[Z==0]\, \M[Z==1]\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# print(\dist. of M based on the G-computation\)
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\G-computation\,col=\green\)
abline(v = 0, col = \black\, lwd = 2)abline(v = 1, col = \black\, lwd = 2)
legend(\topright\, legend=c(\M0\, \Mr\, \M1\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDEwMClcbmhpc3QoTSx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE06IGRhdGFcXClcbmBgYFxuYGBgIn0= -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTBdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0wXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==0]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTFdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0xXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==1]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDM1MClcbmhpc3QoTTBfbWNbd2hpY2goKE0wX21jPnhsaW1fQ0VbMV0pKihNMF9tYzx4bGltX0NFWzJdKT09MSldLDFlMyx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE0wOiBHLWNvbXB1dGF0aW9uXFwpXG5gYGBcbmBgYCJ9 -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M0: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNcl9tY1t3aGljaCgoTXJfbWM+eGxpbV9DRVsxXSkqKE1yX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTXI6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Mr: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNMV9tY1t3aGljaCgoTTFfbWM+eGxpbV9DRVsxXSkqKE0xX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTTE6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M1: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIC0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS1cbiMgLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLVxuIyAtLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tXG5yaG8gPSBcXHVuaWZcXFxuUE9TVHJlc3VsdFJob1VuaWYgPSBFRFBtZWRpYXRpb25QT1NUKE1DTUNyZXN1bHQsIGVzdHR5cGUsIHJobywgc2F2ZV9jbHVzdGVyKVxuYGBgXG5gYGAifQ== -->
```r
```r
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = \unif\
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:32:48 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:32:48 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:32:49 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:32:49 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:32:50 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:32:50 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:32:51 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:32:51 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:32:51 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:32:52 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc
CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c(\NIE\,\NDE\,\ATE\)
NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE
q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col=\red\,ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col=\blue\,ylim=ylim_CE);par(new=T)plot(sort(ATErhoUnif),col=\green\,ylim=ylim_CE)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuQ0VfdGFibGVSaG9VbmlmXG5gYGBcbmBgYCJ9 -->
```r
```r
CE_tableRhoUnif
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiICAgICAgZXN0aW1hdGVzICAgICAgICBzZCBxdWFudGlsZTAyNSBxdWFudGlsZTk3NSBDSWxlbmd0aDk1XG5OSUUgIDAuMDE1MTc2MjIgMC4xMzEwMzEzICAtMC4yODYxMzk4ICAgMC4yMjM4NzQ3ICAwLjUxMDAxNDVcbk5ERSAtMy4xMDg3ODcwNSAwLjcxMDcyNjggIC00LjQ2OTU0OTQgIC0xLjkzMjIyNDEgIDIuNTM3MzI1NFxuQVRFIC0zLjA5MzYxMDg0IDAuNzE1ODE1MyAgLTQuNTMyNDAyNyAgLTEuOTE4NDYxMSAgMi42MTM5NDE2XG4ifQ== -->
estimates sd quantile025 quantile975 CIlength95NIE 0.01517622 0.1310313 -0.2861398 0.2238747 0.5100145 NDE -3.10878705 0.7107268 -4.4695494 -1.9322241 2.5373254 ATE -3.09361084 0.7158153 -4.5324027 -1.9184611 2.6139416
<!-- rnb-output-end -->
<!-- rnb-chunk-end -->
<!-- rnb-text-begin -->
\newpage
### dist. of f(M) = log(1+M)
<!-- rnb-text-end -->
<!-- rnb-chunk-begin -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuc2V0LnNlZWQoMSlcbk0gPSBMSVRFZGF0YSRhdHRcbk0gPSBsb2coMStNKVxuXG5NQ01DcmVzdWx0ID0gRURQbWVkaWF0aW9uTUNNQyhZLCBNLCBWLCBaLCBDLFxuICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgZ2liYnNfaXRlciwgZ2liYnNfYnVybmluLCBnaWJic190aGluLFxuICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgRCwgbnVtX01DLCBudW1fTUNfcHJpb3IpXG5gYGBcbmBgYCJ9 -->
```r
```r
set.seed(1)
M = LITEdata$att
M = log(1+M)
MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
gibbs_iter, gibbs_burnin, gibbs_thin,
D, num_MC, num_MC_prior)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Bur-In End 5000 Time: Tue Feb 21 18:35:50 2023 Gibbs Iteration 250 ( 5 %) Time: Tue Feb 21 18:35:57 2023 Gibbs Iteration 500 ( 10 %) Time: Tue Feb 21 18:36:04 2023 Gibbs Iteration 750 ( 15 %) Time: Tue Feb 21 18:36:12 2023 Gibbs Iteration 1000 ( 20 %) Time: Tue Feb 21 18:36:18 2023 Gibbs Iteration 1250 ( 25 %) Time: Tue Feb 21 18:36:26 2023 Gibbs Iteration 1500 ( 30 %) Time: Tue Feb 21 18:36:33 2023 Gibbs Iteration 1750 ( 35 %) Time: Tue Feb 21 18:36:40 2023 Gibbs Iteration 2000 ( 40 %) Time: Tue Feb 21 18:36:47 2023 Gibbs Iteration 2250 ( 45 %) Time: Tue Feb 21 18:36:55 2023 Gibbs Iteration 2500 ( 50 %) Time: Tue Feb 21 18:37:02 2023 Gibbs Iteration 2750 ( 55 %) Time: Tue Feb 21 18:37:10 2023 Gibbs Iteration 3000 ( 60 %) Time: Tue Feb 21 18:37:17 2023 Gibbs Iteration 3250 ( 65 %) Time: Tue Feb 21 18:37:25 2023 Gibbs Iteration 3500 ( 70 %) Time: Tue Feb 21 18:37:32 2023 Gibbs Iteration 3750 ( 75 %) Time: Tue Feb 21 18:37:39 2023 Gibbs Iteration 4000 ( 80 %) Time: Tue Feb 21 18:37:46 2023 Gibbs Iteration 4250 ( 85 %) Time: Tue Feb 21 18:37:54 2023 Gibbs Iteration 4500 ( 90 %) Time: Tue Feb 21 18:38:01 2023 Gibbs Iteration 4750 ( 95 %) Time: Tue Feb 21 18:38:08 2023 Gibbs Iteration 5000 ( 100 %) Time: Tue Feb 21 18:38:16 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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-->
```r
```r
{
# Significance Level alpha
level = 0.05
quantile_alpha = c(level/2,1-level/2)
# the number of Gibbs Sampler stored
n_MCMC = MCMCresult$constants$n_MCMC
# Define interation check
iter_check = floor(n_MCMC/10)
M0_mc = list(NA)
Mr_mc = list(NA)
M1_mc = list(NA)
N = MCMCresult$constants$N
D = MCMCresult$constants$D
num_MC = MCMCresult$constants$num_MC
p_V = MCMCresult$constants$p_V
p_Z = MCMCresult$constants$p_Z
p_C1 = MCMCresult$constants$p_C1
p_C2 = MCMCresult$constants$p_C2
f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
a_Ysig2 = MCMCresult$priors$a_Ysig2
b_Ysig2 = MCMCresult$priors$b_Ysig2
a_Ybeta = MCMCresult$priors$a_Ybeta
B_Ybeta = MCMCresult$priors$B_Ybeta
a_Msig2 = MCMCresult$priors$a_Msig2
b_Msig2 = MCMCresult$priors$b_Msig2
a_Mbeta = MCMCresult$priors$a_Mbeta
B_Mbeta = MCMCresult$priors$B_Mbeta
a_Vsig2 = MCMCresult$priors$a_Vsig2
b_Vsig2 = MCMCresult$priors$b_Vsig2
a_Vbeta = MCMCresult$priors$a_Vbeta
B_Vbeta = MCMCresult$priors$B_Vbeta
a_pi = MCMCresult$priors$a_pi
b_pi = MCMCresult$priors$b_pi
a_mu = MCMCresult$priors$a_mu
b_mu = MCMCresult$priors$b_mu
a_tau2 = MCMCresult$priors$a_tau2
b_tau2 = MCMCresult$priors$b_tau2
alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
rho = runif(n_MCMC)
# End initial values ------------------------------------------------------------
for (post_reps in 1:n_MCMC) {
Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
rho_mc = rho[post_reps] * rep(1,D)
YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
ZpiPars_array = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
XpiPars_array = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
XmuPars_array = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
alpha_theta = alpha_theta_draws[post_reps]
alpha_omega = alpha_omega_draws[post_reps]
MCresult = EDPpostmc_concon(p_C1, p_C2,
n_k, n_rk, Ky, Kyx, max_Kx_Sy,
D, num_MC, rho_mc,
YbetaPars, Ysig2Pars,
MbetaPars, Msig2Pars,
VbetaPars_array, Vsig2Pars_array,
ZpiPars_array, XpiPars_array,
XmuPars_array, Xtau2Pars_array,
alpha_theta, alpha_omega,
f0_z0_mc, f0_z1_mc,
YbetaPrior_mc,
MbetaPrior_mc, Msig2Prior_mc,
VbetaPrior_mc, Vsig2Prior_mc,
a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
M0_mc[[post_reps]] = MCresult$M0_mc
Mr_mc[[post_reps]] = MCresult$Mr_mc
M1_mc[[post_reps]] = MCresult$M1_mc
if (post_reps %% iter_check == 0){
cat(\Post-Processing\,post_reps,\(\,(post_reps/n_MCMC)*100,\%)\,\Time:\,date(),\\n\)
}
}
distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:38:17 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:38:17 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:38:18 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:38:18 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:38:19 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:38:19 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:38:20 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:38:20 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:38:20 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:38:21 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTTBfbWMgPSB1bmxpc3QoZGlzdE0kTTBfbWMpXG5Ncl9tYyA9IHVubGlzdChkaXN0TSRNcl9tYylcbk0xX21jID0gdW5saXN0KGRpc3RNJE0xX21jKVxuXG5tZWFuKE0pXG5gYGBcbmBgYCJ9 -->
```r
```r
M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)
mean(M)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuMzk4MzEyOFxuIn0= -->
[1] 0.3983128
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTBdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==0])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuMzg5NTkxNVxuIn0= -->
[1] 0.3895915
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTFdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==1])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuNDA3Njg0NFxuIn0= -->
[1] 0.4076844
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)
# print(\dist. of M based on the data\)
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Data\,col=\green\)
legend(\topright\, legend=c(\M\, \M[Z==0]\, \M[Z==1]\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# print(\dist. of M based on the G-computation\)
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\G-computation\,col=\green\)
abline(v = 0, col = \black\, lwd = 2)abline(v = 1, col = \black\, lwd = 2)
legend(\topright\, legend=c(\M0\, \Mr\, \M1\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDEwMClcbmhpc3QoTSx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE06IGRhdGFcXClcbmBgYFxuYGBgIn0= -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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Q3t7OwMlrj0xJmoaWhnZ2ewxKUnzkRNQzs7O4MlLj1xJmoa2tnZGSxx6YkzUdPQzs7OYIlLT5yJmoZ2dnYGS1x64kzUNLSzszNY4tITZ6KmoZ2dncESl544EzUN7ezsDJa49MSZqGloZ2dnsMSlJ85ETUM7OzuDJS49cSZqGtrZ2RkscemJM1HT0M7OzmCJS0+ciZqGdnZ2BktceuJM1DS0s7MzWOLSE2eipqGdnZ3BEpeeOBM1De3s7AyWuPTEmahpaGdnZ7DEpSfORE1DOzs7gyUuPXEmahra2dkZLHHpiTNR09DOzs5giUtPnImahnZ2dgZLXHriTNQ0tLOzM1ji0hNnoqahnZ2dwRKXnjgTNQ3t7OwMlrj0xJmoaWhnZ2ewxKUnzkRNQzs7O4MlLj1xJmoa2tnZGSxx6YkzUdPQzs7OYIlLT5yJmoZ2dnYGS1x64kzUNLSzszNY4tITZ6KmoZ2dncESl544EzUN7ezsDJa49MSZqGloZ2dnsMSlJ85ETUM7OzuDJS49cSZqGtrZ2RkscemJM1HT0M7OzmCJS0+ciZqGdnZ2BktceuJM1DS0s7MzWOLSE2eipqGdnZ3BEpeeOBM1De3s7AyWuPTEmahpaGdnZ7DEpSfORE1DOzs7gyUuPXEmahra2dkZLHHpiTNR09DOzs5goy391ePD+3fX7h0++m3gXV2I86GhnZ2dwUZa+tOPVhvufJUwEyPQ0M7OzmCjLP3469U1HzybeiZGoaGdnZ3Bxlj6WULvfXvxKfyrn+8PjKgLcT40tLOzM9gYS3+y/uz9weYNTw9Wq89vf38X4nxoaGdnZ7ARln76MvRaMZ8MeiHqQpwPDe3s7Aw2wtJ//2J157vtm14crN776dYP4EKcDw3t7OwMNk5DrwezuOktXIjzoaGdnZ3BvA7lj9DQzs7OYGMs/eiNr4eub/nw9vd3Ic6HhnZ2dgYbY+nPV6vVZxvfQjr+2/qGBzd//HUuxPnQ0M7OzmCjLP3o9MfqP370w69r/3z88GA16GWohs6IhnZ2dgYbZ+lPrv+e0qfTz8QYNLSzszPYSEt/+XCzoJ/8mDATI9DQzs7OYOMt/dUvj785PPzy0d+Hvm2Ths6IhnZ2dgZLXHriTNQ0tLOzM9j0S7/+pdO1qUfi1jS0s7Mz2FhLP/6/Zz/cdPz9/bt3P/l22H1diPOhoZ2dncHGWfrLP5//XtI/Ds5fWL7/3c67jD4TY9DQzs7OYKMs/fk6nacN3fgRpwE/Yq+hM6KhnZ2dwcZY+ot1Qv/0r8/O/veDH89elQ75dXkNnREN7ezsDDbS78ufvVvo5f9W7yi675kYh4Z2dnYGG+k9mB9s/O/J2W/Qew/mLmloZ2dnsBHfP3TjTUO9f2ivNLSzszOYhvJHaGhnZ2ewcT6XP38P5qOr92J+ceBz+T5paGdnZ7CR/l3Ps2I+v/pO0hPvwdwpDe3s7Aw21s82fXj+jfnzF6JPvQdzrzS0s7Mz2ChLP/3Z+jv/8sPZZ/Wf/M/H970Hc7c0tLOzM9g4S7/8Hc8rH97+q6EaOica2tnZGWwv78F856uEmRiBhnZ2dgYbb+n//P7w7qnDfx/2LvYaOica2tnZGSxx6YkzUdPQzs7OYIlLT5yJmoZ2dnYGS1x64kzUNLSzszNY4tITZ6KmoZ2dncESl544EzUN7ezsDJa49MSZqGloZ2dnsMSlJ85ETUM7OzuDJS49cSZqGtrZ2RkscemJM1HT0M7OzmCJS0+ciZqGdnZ2BktceuJM1DS0s7MzWOLSE2eipqGdnZ3BEpeeOBM1De3s7AyWuPTEmahpaGdnZ7DEpSfORE1DOzs7gyUuPXEmahra2dkZLHHpiTNRm6Khq8K7/QM0lNtLXHriTNQmaejYf6aGMkDi0hNnoqahGrp0iUtPnImahmro0iUuPXEmahqqoUuXuPTEmahpqIYuXeLSE2eipqEaunSJS0+ciZqGaujSJS49cSZqGqqhS5e49MSZqGmohi5d4tITZ6KmoRq6dIlLT5yJmoZq6NIlLj1xJmoaqqFLl7j0xJmoaaiGLl3i0hNnoqahGrp0iUtPnImahmro0iUuPXEmahqqoUuXuPTEmahpqIYuXeLSE2eipqEaunSJS0+ciZqGaujSJS49cSZqGqqhS5e49MSZqGmohi5d4tITZ6KmoRq6dIlLT5yJmoZq6NIlLj1xJmoaqqFLl7j0xJmoaaiGLl3i0hNnoqahGrp0iUtPnImahmro0iUuPXEmahqqoUuXuPTEmahpqIYuXeLSE2eipqEaunSJS0+ciZqGaujSJS49cSZqGqqhS5e49MSZqGmohi5d4tITZ6KmoRq6dIlLT5yJmoZq6NIlLj1xJmoaqqFLl7j0xJmoaaiGLl3i0hNnoqahGrp0iUtPnImahmro0iUuPXEmahqqoUuXuPTEmahpqIYuXeLSE2eipqEaunSJS0+ciZqGaujSJS49cSZqGqqhS5e49MSZqGmohi5d4tITZ6KmoRq6dIlLT5yJmoZq6NIlLj1xJmoaqqFLl7j0xJmoaaiGLl3i0hNnoqahGrp0iUtPnImahmro0iUuPXEmahqqoUuXuPTEmahpqIYuXeLSE2eipqEaunSJS0+ciZqGaujSJS49cSZqGqqhS5e49MSZqGmohi5d4tITZ6KmoRq6dKMt/dXjw/t31+4dPvpt4F1diPOhoRq6dCMt/elHqw13vkqYiRFoqIYu3ShLP/56dc0Hz6aeiVFoqIYu3RhLP0vovW8vPoV/9fP9gRF1Ic6Hhmro0o2x9Cfrz94fbN7w9GC1+vz293chzoeGaujSjbD005eh14r5ZNALURfifLzTnl3/CtCZkf/Mcg4N5fZGWPrvX6zufLd904uD1Xs/3foBXIjz8W4bersqaShJxmno9WAWN72FC3E+NFRDl87rUP4IDdXQpRtj6UdvfD10fcuHt7+/C3E+NFRDl26MpT9frVafbXwL6fhv6xse3Pzx17kQ50NDNXTpRln60en3Uz9+9MOva/98/PBgNehlqIbOiIZq6NKNs/Qn139A5dPpZ2IMGqqhSzfS0l8+3CzoJz8mzMQINFRDl268pb/65fE3h4dfPvr70Ldt0tAZ0VANXbrEpSfORE1DNXTppl/6rX69j1DBDb3dL47e9lAayg1GX/rv9+/eu/2P159xIc5HckObR9NQBhi/oYN+zfOMC3E+NFRDl05D+SM0VEOXbozflz/7d5Qunf6jIH86/XeV/L58jzRUQ5dunPccKXjPkS5pqIYu3UjvwayhC6GhGrp0oyz9HwerO99e/N++Hto1DdXQpRtn6S//vFp9ev7OTRraNQ3V0KUbaenHf12t3j/7LXkN7ZqGaujSjbb0p+vP57860dDOaaiGLt14S3/59Wr1yTMN7ZuGaujSjbj007evv/OthnZNQzV06UZd+ouD1epjDe2Zhmro0o279OOHA3809IwLcT40VEOXbuylPz3Q0J5pqIYu3ehLf/nN4ZfPdn/YJhfifGiohi5d4tITZ6KmoRq6dIlLT5yJmoZq6NIlLj1xJmoaqqFLl7j0xJmoaaiGLl3i0hNnoqahGrp0iUtPnImahmro0iUuPXEmahqqoUuXuPTEmahpqIYuXeLSE2eipqEaunSJS0+ciZqGaujSJS49cSZqGqqhS5e49MSZqGmohi5d4tITZ6KmoRq6dIlLT5yJmoZq6NIlLj1xJmoaqqFLl7j0xJmoaaiGLl3i0hNnoqahGrp0iUtPnImahmro0iUuPXEmahqqoUuXuPTEmahpqIYuXeLSE2eipqEaunSJS0+ciZqGaujSJS49cSZqGqqhS5e49MSZqGmohi5d4tITZ6KmoRq6dIlLT5yJmoZq6NIlLj1xJmoaqqFLl7j0xJmoaaiGLl3i0hNnoqahGrp0iUtPnImahmro0iUuPXEmarftWeFWD6ahpEtceuJM1N5pzzSUGUpceuJM1DS05Q+gJ4lLT5yJmoa2/AH0JHHpiTNR09CWP4CeJC49cSZqGtryB9CTxKUnzkRtZg291Y8HaChDJC49cSZqM2voO73n7aald4lLT5yJmobufDQ6l7j0xJmoaejOR6NziUtPnImahu58NDqXuPTEmahp6M5Ho3OJS0+ciZqG7nw0Ope49MSZqGnozkejc4lLT5yJmobufDQ6l7j0xJmoaejOR6NziUtPnImahu58NDqXuPTEmahp6M5Ho3OJS0+ciZqG7nw0Ope49MSZqGnozkejc4lLT5yJmobufDQ6l7j0xJmoaejOR6NziUtPnImahu58NDqXuPTEmahp6M5Ho3OJS0+ciZqG7nw0Ope49MSZqGnozkejc4lLT5yJmobufDQ6l7j0xJmoaejOR6NziUtPnImahu58NDqXuPTEmahp6M5Ho3OJS0+ciZqG7nw0Ope49MSZqGnozkejc4lLT5yJmobufDQ6l7j0xJmoaejOR6NziUtPnImahu58NDqXuPTEmahp6M5Ho3OJS0+ciZqG7nw0Ope49MSZqGnozkejc4lLT5yJmobufDQ6l7j0xJmoaejOR6NziUtPnImahu58NDqXuPTEmahp6M5Ho3OJS0+ciZqG7nw0Ojfa0l89Prx/d+3e4aPfBt7VhTgfGrrz0ejcSEt/+tFqw52vEmZiBBq689Ho3ChLP/56dc0Hz6aeiVFo6M5Ho3NjLP0sofe+vfgU/tXP9wdG1IU4Hxq689Ho3BhLf7L+7P3B5g1PD1arz29/fxfifGjozkejcyMs/fRl6LViPhn0QtSFOB/zb2jldve83bT0boSl//7F6s532ze9OFi999OtH8CFOB/zb2j1Z7bf848+n8zPOA29HsziprdwIc6Hhu6cg855HcofoaE756BzYyz96I2vh65v+fD293chzoeG7pyDzo2x9Oer1eqzjW8hHf9tfcODmz/+OhfifGjozjno3ChLPzr93ubHj374de2fjx8erAa9DNXQGdHQnXPQuXGW/uT6D4t8Ov1MjEFDd85B50Za+suHmwX95MeEmRiBhu6cg86Nt/RXvzz+5vDwy0d/H/q2TRo6Ixq6cw46l7j0xJmoaejOOejc9EsvftVu6pG4NQ3dOQedG23pv/66+dNN3xx+6ffle6ShO+egc+Ms/fxbSu9/e/nfftezVxq6cw46N8rSXxxce+tlDe2Vhu6cg86NsfR1MVerjw//8+lL0Z8ub9HQLmnozjno3FjvwXz6piMvv15dpFNDe6WhO+egc6O+B/Px0cWn8xraKw3dOQedG/e9744v3rBJQ3uloTvnoHMjvwfzxWtSDe2Vhu6cg86N/T725y9KNbRXGrpzDjo3ztdDN97H/vnp95U0tFcaunMOOjfS9+U/3PqvD/6fhnZKQ3fOQefGWPrpj9hvvI/9OqJ/WmlonzR05xx0bpSln74F80Yzz96RWUO7pKE756Bz4yz9H9v/jufTAw3tlIbunIPOjbT045+33qfp+PsDDe2Shu6cg84lLj1xJmrjN7TQ/mfesoTt93zXzy/5EpeeOBO18Rt6u5tu+Wfe6iYNZYjEpSfORE1Dd85B5xKXnjgTNQ3dOQedS1x64kzUNHTnHHQucemJM1HT0J1z0LnEpSfORE1Dd85B5xKXnjgTNQ3dOQedS1x64kzUNHTnHHQucemJM1HT0J1z0LnEpSfORE1Dd85B5xKXnjgTNQ3dOQedS1x64kzUNHTnHHQucemJM1HT0J1z0LnEpSfORE1Dd85B5xKXnjgTNQ3dOQedS1x64kzUNHTnHHQucemJM1HT0J1z0LnEpSfORE1Dd85B5xKXnjgTNQ3dOQedS1x64kzUNHTnHHQucemJM1HT0J1z0LnEpSfORE1Dd85B5xKXnjgTNQ3dOQedS1x64kzUNHTnHHQucemJM1HT0J1z0LnEpSfORC2loZXWB9NQhkhceuJM1FIamnLP0Z9w4iQuPXEmahq6fdvoTzhxEpeeOBM1Dd2+bfQnnDiJS0+ciZqGbt82+hNOnMSlJ85ETUO3bxv9CSdO4tITZ6Kmodu3jf6EEydx6YkzUdPQ7dtGf8KJk7j0xJmoaej2baM/4cRJXHriTNQ0dPu20Z9w4iQuPXEmahq6fdvoTzhxEpeeOBM1Dd2+bfQnnDiJS0+ciZqGbt82+hNOnMSlJ85ETUO3bxv9CSdO4tITZ6Kmodu3jf6EEydx6YkzUdPQ7dtGf8KJk7j0xJmoaej2baM/4cRJXHriTNQ0dPu20Z9w4iQuPXEmahq6fdvoTzhxEpeeOBM1Dd2+bfQnnDiJS0+ciZqGbt82+hNOnMSlJ85ETUO3bxv9CSdO4tITZ6Kmodu3jf6EE7SBYAIAAAoeSURBVCdx6YkzUdPQ7dtGf8KJk7j0xJmoaej2baM/4cRJXHriTNQ0dPu20Z9w4iQuPXEmahq6fdvoTzhxEpeeOBO1qi2V233Yu+3ZFPeceh/sX+LSE2eiltyzKe459T7Yv8SlJ85ELblnU9xz6n2wf4lLT5yJWnLPprjn1Ptg/xKXnjgTteSeTXHPqffB/iUuPXEmask9m+KeU++D/UtceuJM1JJ7NsU9p94H+5e49MSZqCX3bIp7Tr0P9i9x6YkzUUvu2RT3nHof7F/i0hNnopbcsynuOfU+2L/EpSfORC25Z1Pcc+p9sH+JS0+ciVpyz6a459T7YP8Sl544E7Xknk1xz6n3wf4lLj1xJmrJPZvinlPvg/1LXHriTNSSezbFPafeB/uXuPTEmagl92yKe069D/YvcemJM1FL7tkU95x6H+xf4tITZ6KW3LMp7jn1Pti/xKUnzkQtuWdT3HPqfbB/iUtPnIlacs+muOfU+2D/EpeeOBO15J5Ncc+p98H+JS49cSZqyT2b4p5T74P9S1x64kzUkns2xT2n3gf7l7j0xJmoJfdsintOvQ/2L3HpiTNRS+7ZFPeceh/sX+LSE2eiltyzKe459T7Yv8SlJ85ELblnU9xz6n2wf4lLT5yJWnLPprjn1Ptg/xKXnjgTteSeTXHPqffB/iUuPXEmask9m+KeU++D/Rtt6a8eH96/u3bv8NFvA+/qQpyP5J5Ncc+p98H+jbT0px+tNtz5KmEmRpDcsynuOfU+2L9Rln789eqaD55NPROjSO7ZFPeceh/s3xhLP0vovW8vPoV/9fP9gRF1Ic5Hcs+muOfU+2D/xlj6k/Vn7w82b3h6sFp9fvv7uxDnI7lnU9xz6n2wfyMs/fRl6LViPhn0QtSFOB/JPZvinlPvg/0bYem/f7G68932TS8OVu/9dOsHcCHOR3LPprjn1Ptg/8Zp6PVgFje9nuBN734mRlJsb9Gm3gf7l/g6FGAuxviL8+iNr4eub/lwhD8IYGJjNPT5+nOazza+hXT8t/UND27+eIC5GuULOEenXxn6+NEPv6798/HDg5WXoUCfxvki+JPrX2r/dJQ/BmBiI30j8eXDzYJ+8uM4fwrAxMb7YYxXvzz+5vDwy0d/H/q2TQCz4QfaANppKEA7DQVop6EA7TQUoJ2GArTTUIB2GgrQTkMB2mkoQDsNBWinoQDtNBSg3bwbupd/ZgwY09QZ+YPmPf+8pz9xgOk5wOTmfoJ5zz/v6U8cYHoOMLm5n2De8897+hMHmJ4DTG7uJ5j3/POe/sQBpucAk5v7CeY9/7ynP3GA6TnA5OZ+gnnPP+/pTxxgeg4wubmfYN7zz3v6EweYngNMbu4nmPf8857+xAGm5wCTm/sJ5j3/vKc/cYDpOcDk5n6Cec8/7+lPHGB6DjC5uZ9g3vPPe/oTB5ieA0xu7ieY9/zznv7EAabnAJOb+wnmPf+8pz9xgOk5wOTmfoJ5zz/v6U8cYHoOMLm5n2De8897+hMHmJ4DTG7uJ5j3/POe/sQBpucAk5v7CeY9/7ynP3GA6TnA5OZ+gnnPP+/pTxxgeg4wubmfYO7zA0xJQwHaaShAOw0FaKehAO00FKCdhgK001CAdhoK0E5DAdppKEA7DQVop6EA7TQUoJ2GArTTUIB2GgrQTkMB2mkoQDsNBWinoQDtNBSgnYYCtNNQgHYaCtBung09Wn1e3Prz/dVqde/bvU8z0E1jvjhYXapOF+Hmp9iTvz+zvvzPVCeY1Qo2zbKhz6tn+fivFwv49NkEI93azWM+X6VfQzfP7snfozlf/ufKE8xpBVvm2NDnB9WzfHS1gQ8nmOnWbh7zSfw1dPPsnvz9mfXlf6Y+wYxWsG2GDX16UD3Lp58JfPbs7K/jO99NMdbtvGXMo9V7P00z1C3dPLsnf39mffmfqU8woxVcM7uGvnxY/011dHnbk+i/iW8e8/jr1QfZn4bdPLsnf19mfvmf3HyC2azgDXNr6JP132Hv/8ebK/j9i8u/xda7yP377C1jrl9JZH8Kc/Psnvx9mfnlf3LzCWazgjfNraFHqzt/eVZ8SXq9gcu/ftd/Ez/Y91i39ZYxnwePfebm2T35+zLzy//k5hPMZgVvml1DP/2t/LbexgaSl/GWMZ+s7nz39KPV6k9/Cf2M5ubZPfn7MvPL/+TmE8xmBW+aW0PPFCvY+Ns3+ZOCt4y5/gv6o/PvSoZ+U+Dm2T35ezXfy/9S1dBZrWBLPw29euaTL6Kbx/z9i9c/2pF5Ed08uyd/r+Z7+V8qTjCvFWzppaFHWxdR7Hcmbx5z/Z93/rL+NOf49Cc/Ir9BefPsnvy9mu/lf6n+iu6MVrBFQ/fqNmO+/CLzL+KOG/pa6pO/ab6X/6Xy95QuzWEFW2bQ0MtX+a9/ZGNmn8xsHOBWYz7J/EWNjj+X3/qg3ANcmNnlX3hrQ+ewgi39NDT3i+pbDb3FmKGvJHr+ntJroU/+ppld/oW3N3QGK9jSS0OTf7hj4wC3GjP0Gur5Z5teC33yN83s8i9o6OTqL0lf3vQk+Msptxrz7VfYZG6e3ZO/V/O9/C+9/UmewQq29NLQ9Wu9i2/mRf+y281jbnw2dpT5SuLm2T35ezXfy//S278aMYMVbOmloXN504Ubx3x+9RMdz1eh/6+g3/ccmcGTv2HGl/+F+qsRM1rBlm4aevrmX5/mv/nXjWOuXz+s3v9h/b/fl2+umODmp9iTv08zvvwvFCeY1wq2zL2hr9+wZiZvQnt9zKsDbLyNd+qPGN84uyd/n+Z8+Z+rTjCrFWzpp6Ez+ccQro/5+gBPD9IvoZtn9+Tv0Zwv/3PlCea0gi39NHQ2/yjX9pgbBzj+/qP0A9w4uyd/f+Z9+Z+qTzCjFWyZZUMBQmgoQDsNBWinoQDtNBSgnYYCtNNQgHYaCtBOQwHaaShAOw0FaKehAO00FKCdhgK001CAdhoK0E5DAdppKEA7DQVop6EA7TQUoJ2GArTTUIB2GgrQTkMB2mkoQDsNBWinoQDtNBSgnYYCtNNQgHYaCtBOQwHaaShAOw0FaKehAO00FKCdhgK001CAdhoK0E5DAdppKEA7DQVop6EA7TQUoJ2GArTTUIB2GgrQTkMB2mkoQDsNBWinoQDtNBSgnYYCtNNQgHYaCtBOQwHaaShAOw0FaKehAO00FKCdhgK001CAdhoK0E5DAdppKEA7DQVop6EA7TQUoJ2GArTTUIB2GgrQTkMB2mkoQDsNBWinoQDtNBSgnYYCtNNQgHYaCtBOQwHaaShAOw0FaKehAO00FKCdhgK001CAdhoK0E5DAdppKEA7DQVop6EA7TQUoJ2GArTTUIB2GgrQTkMB2mkoQDsNBWinoQDtNBSgnYYCtNNQgHYaCtBOQwHaaShAOw0FaKehAO00FKCdhgK001CAdhoK0E5DAdppKEA7DQVop6EA7TQUoJ2GArT7/2X9UPToMTj5AAAAAElFTkSuQmCC" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTBdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0wXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==0]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTFdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0xXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==1]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDM1MClcbmhpc3QoTTBfbWNbd2hpY2goKE0wX21jPnhsaW1fQ0VbMV0pKihNMF9tYzx4bGltX0NFWzJdKT09MSldLDFlMyx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE0wOiBHLWNvbXB1dGF0aW9uXFwpXG5gYGBcbmBgYCJ9 -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M0: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNcl9tY1t3aGljaCgoTXJfbWM+eGxpbV9DRVsxXSkqKE1yX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTXI6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Mr: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNMV9tY1t3aGljaCgoTTFfbWM+eGxpbV9DRVsxXSkqKE0xX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTTE6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M1: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIC0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS1cbiMgLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLVxuIyAtLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tXG5yaG8gPSBcXHVuaWZcXFxuUE9TVHJlc3VsdFJob1VuaWYgPSBFRFBtZWRpYXRpb25QT1NUKE1DTUNyZXN1bHQsIGVzdHR5cGUsIHJobywgc2F2ZV9jbHVzdGVyKVxuYGBgXG5gYGAifQ== -->
```r
```r
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = \unif\
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:38:25 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:38:25 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:38:26 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:38:26 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:38:27 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:38:27 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:38:28 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:38:28 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:38:29 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:38:29 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc
CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c(\NIE\,\NDE\,\ATE\)
NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE
q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col=\red\,ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col=\blue\,ylim=ylim_CE);par(new=T)plot(sort(ATErhoUnif),col=\green\,ylim=ylim_CE)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuQ0VfdGFibGVSaG9VbmlmXG5gYGBcbmBgYCJ9 -->
```r
```r
CE_tableRhoUnif
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiICAgICAgZXN0aW1hdGVzICAgICAgICBzZCBxdWFudGlsZTAyNSBxdWFudGlsZTk3NSBDSWxlbmd0aDk1XG5OSUUgLTAuMDkxNjIyMDYgMC4xMTg2MDI5ICAtMC4zNzA2MjcyICAwLjA1NDMzNDQ5ICAwLjQyNDk2MTdcbk5ERSAtMy4zMTgxMjg0MyAwLjcwMjQwMzEgIC00Ljg4MjU5NTUgLTIuMTg1OTM4MzEgIDIuNjk2NjU3MlxuQVRFIC0zLjQwOTc1MDUwIDAuNjk2MTg2MyAgLTQuOTQ2NTE2MCAtMi4zMzI5NTI3MiAgMi42MTM1NjMzXG4ifQ== -->
estimates sd quantile025 quantile975 CIlength95NIE -0.09162206 0.1186029 -0.3706272 0.05433449 0.4249617 NDE -3.31812843 0.7024031 -4.8825955 -2.18593831 2.6966572 ATE -3.40975050 0.6961863 -4.9465160 -2.33295272 2.6135633
<!-- rnb-output-end -->
<!-- rnb-chunk-end -->
<!-- rnb-text-begin -->
\newpage
### dist. of f(M) = invlogit(M)
<!-- rnb-text-end -->
<!-- rnb-chunk-begin -->
<!-- rnb-source-begin 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 -->
```r
```r
set.seed(1)
M = LITEdata$att
M = as.numeric(scale(M))
M = exp(M)
M = log(1+M)
M = invlogit(M)
eps = 0.1
M = (M*(diff(range(M))-2*eps))+eps
eps = 0.1
M = (M*(diff(range(M))-2*eps))+eps
M = log(M/(1-M))
MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
gibbs_iter, gibbs_burnin, gibbs_thin,
D, num_MC, num_MC_prior)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Bur-In End 5000 Time: Tue Feb 21 18:41:23 2023 Gibbs Iteration 250 ( 5 %) Time: Tue Feb 21 18:41:31 2023 Gibbs Iteration 500 ( 10 %) Time: Tue Feb 21 18:41:39 2023 Gibbs Iteration 750 ( 15 %) Time: Tue Feb 21 18:41:46 2023 Gibbs Iteration 1000 ( 20 %) Time: Tue Feb 21 18:41:53 2023 Gibbs Iteration 1250 ( 25 %) Time: Tue Feb 21 18:42:01 2023 Gibbs Iteration 1500 ( 30 %) Time: Tue Feb 21 18:42:08 2023 Gibbs Iteration 1750 ( 35 %) Time: Tue Feb 21 18:42:16 2023 Gibbs Iteration 2000 ( 40 %) Time: Tue Feb 21 18:42:23 2023 Gibbs Iteration 2250 ( 45 %) Time: Tue Feb 21 18:42:31 2023 Gibbs Iteration 2500 ( 50 %) Time: Tue Feb 21 18:42:39 2023 Gibbs Iteration 2750 ( 55 %) Time: Tue Feb 21 18:42:46 2023 Gibbs Iteration 3000 ( 60 %) Time: Tue Feb 21 18:42:54 2023 Gibbs Iteration 3250 ( 65 %) Time: Tue Feb 21 18:43:01 2023 Gibbs Iteration 3500 ( 70 %) Time: Tue Feb 21 18:43:09 2023 Gibbs Iteration 3750 ( 75 %) Time: Tue Feb 21 18:43:16 2023 Gibbs Iteration 4000 ( 80 %) Time: Tue Feb 21 18:43:24 2023 Gibbs Iteration 4250 ( 85 %) Time: Tue Feb 21 18:43:31 2023 Gibbs Iteration 4500 ( 90 %) Time: Tue Feb 21 18:43:39 2023 Gibbs Iteration 4750 ( 95 %) Time: Tue Feb 21 18:43:46 2023 Gibbs Iteration 5000 ( 100 %) Time: Tue Feb 21 18:43:54 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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-->
```r
```r
{
# Significance Level alpha
level = 0.05
quantile_alpha = c(level/2,1-level/2)
# the number of Gibbs Sampler stored
n_MCMC = MCMCresult$constants$n_MCMC
# Define interation check
iter_check = floor(n_MCMC/10)
M0_mc = list(NA)
Mr_mc = list(NA)
M1_mc = list(NA)
N = MCMCresult$constants$N
D = MCMCresult$constants$D
num_MC = MCMCresult$constants$num_MC
p_V = MCMCresult$constants$p_V
p_Z = MCMCresult$constants$p_Z
p_C1 = MCMCresult$constants$p_C1
p_C2 = MCMCresult$constants$p_C2
f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
a_Ysig2 = MCMCresult$priors$a_Ysig2
b_Ysig2 = MCMCresult$priors$b_Ysig2
a_Ybeta = MCMCresult$priors$a_Ybeta
B_Ybeta = MCMCresult$priors$B_Ybeta
a_Msig2 = MCMCresult$priors$a_Msig2
b_Msig2 = MCMCresult$priors$b_Msig2
a_Mbeta = MCMCresult$priors$a_Mbeta
B_Mbeta = MCMCresult$priors$B_Mbeta
a_Vsig2 = MCMCresult$priors$a_Vsig2
b_Vsig2 = MCMCresult$priors$b_Vsig2
a_Vbeta = MCMCresult$priors$a_Vbeta
B_Vbeta = MCMCresult$priors$B_Vbeta
a_pi = MCMCresult$priors$a_pi
b_pi = MCMCresult$priors$b_pi
a_mu = MCMCresult$priors$a_mu
b_mu = MCMCresult$priors$b_mu
a_tau2 = MCMCresult$priors$a_tau2
b_tau2 = MCMCresult$priors$b_tau2
alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
rho = runif(n_MCMC)
# End initial values ------------------------------------------------------------
for (post_reps in 1:n_MCMC) {
Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
rho_mc = rho[post_reps] * rep(1,D)
YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
ZpiPars_array = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
XpiPars_array = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
XmuPars_array = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
alpha_theta = alpha_theta_draws[post_reps]
alpha_omega = alpha_omega_draws[post_reps]
MCresult = EDPpostmc_concon(p_C1, p_C2,
n_k, n_rk, Ky, Kyx, max_Kx_Sy,
D, num_MC, rho_mc,
YbetaPars, Ysig2Pars,
MbetaPars, Msig2Pars,
VbetaPars_array, Vsig2Pars_array,
ZpiPars_array, XpiPars_array,
XmuPars_array, Xtau2Pars_array,
alpha_theta, alpha_omega,
f0_z0_mc, f0_z1_mc,
YbetaPrior_mc,
MbetaPrior_mc, Msig2Prior_mc,
VbetaPrior_mc, Vsig2Prior_mc,
a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
M0_mc[[post_reps]] = MCresult$M0_mc
Mr_mc[[post_reps]] = MCresult$Mr_mc
M1_mc[[post_reps]] = MCresult$M1_mc
if (post_reps %% iter_check == 0){
cat(\Post-Processing\,post_reps,\(\,(post_reps/n_MCMC)*100,\%)\,\Time:\,date(),\\n\)
}
}
distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:43:55 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:43:56 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:43:56 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:43:56 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:43:57 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:43:57 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:43:58 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:43:58 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:43:59 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:43:59 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTTBfbWMgPSB1bmxpc3QoZGlzdE0kTTBfbWMpXG5Ncl9tYyA9IHVubGlzdChkaXN0TSRNcl9tYylcbk0xX21jID0gdW5saXN0KGRpc3RNJE0xX21jKVxuXG5tZWFuKE0pXG5gYGBcbmBgYCJ9 -->
```r
```r
M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)
mean(M)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIC0yLjU0OTg3MVxuIn0= -->
[1] -2.549871
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTBdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==0])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIC0yLjU0OTkwOFxuIn0= -->
[1] -2.549908
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTFdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==1])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIC0yLjU0OTgzMVxuIn0= -->
[1] -2.549831
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)
# print(\dist. of M based on the data\)
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Data\,col=\green\)
legend(\topright\, legend=c(\M\, \M[Z==0]\, \M[Z==1]\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# print(\dist. of M based on the G-computation\)
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\G-computation\,col=\green\)
abline(v = 0, col = \black\, lwd = 2)abline(v = 1, col = \black\, lwd = 2)
legend(\topright\, legend=c(\M0\, \Mr\, \M1\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDEwMClcbmhpc3QoTSx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE06IGRhdGFcXClcbmBgYFxuYGBgIn0= -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTBdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0wXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==0]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTFdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0xXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==1]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDM1MClcbmhpc3QoTTBfbWNbd2hpY2goKE0wX21jPnhsaW1fQ0VbMV0pKihNMF9tYzx4bGltX0NFWzJdKT09MSldLDFlMyx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE0wOiBHLWNvbXB1dGF0aW9uXFwpXG5gYGBcbmBgYCJ9 -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M0: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNcl9tY1t3aGljaCgoTXJfbWM+eGxpbV9DRVsxXSkqKE1yX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTXI6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Mr: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNMV9tY1t3aGljaCgoTTFfbWM+eGxpbV9DRVsxXSkqKE0xX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTTE6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M1: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIC0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS1cbiMgLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLVxuIyAtLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tXG5yaG8gPSBcXHVuaWZcXFxuUE9TVHJlc3VsdFJob1VuaWYgPSBFRFBtZWRpYXRpb25QT1NUKE1DTUNyZXN1bHQsIGVzdHR5cGUsIHJobywgc2F2ZV9jbHVzdGVyKVxuYGBgXG5gYGAifQ== -->
```r
```r
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = \unif\
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:44:04 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:44:05 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:44:05 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:44:05 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:44:06 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:44:06 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:44:07 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:44:07 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:44:08 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:44:08 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc
CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c(\NIE\,\NDE\,\ATE\)
NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE
q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col=\red\,ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col=\blue\,ylim=ylim_CE);par(new=T)plot(sort(ATErhoUnif),col=\green\,ylim=ylim_CE)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
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CAmkjwAAADERJIHAACAmEjyAAAAEBNJHgAAAGIiyQMAAEBMJHkAAACIiSQPAAAAMXkln8vUarXmvfHx8XwuCQAAAFyUek6+VttcW1iYmalUKpVKZeJE4+eZmYW1tc1a98sAAAAAvajU6/Xezqhtrj24f2d9N+Hh1fnVu+8vzpmoz1ul0vvvDgAAYNSVISv18g7bZvhqtRqmp6dbHtnb2wu7u+eOkufzVoZPJwAAQK/KkJUSvsPa5to7N+4cp/Nqdf6tuzffnJjruCe+Vtv86KOnj1uif3X+2aOH4nw+yvDpBAAA6FUZslKCd1jbXHjnRiOOp5tar9U2H7xzf323eQlpPhdl+HQCAAD0qgxZqes73Fyo3FjPZXn86eL8+Wf1h3MZrkQox6cTAACgV2XISgmS/MzTa11DfPIudLXNhXee3tyR5LMqw6cTAACgV2XISqnfYa22+dGDp4/31nfbVbGvVuffeuvmm2rc9U8ZPp0AAAC9KkNW6voOa5sL79zfm56evnazMTGvC91wKMOnEwAAoFdlyEpJ98mHMP/s8OZnutANjTJ8OgEAAHpVhqyUPMlfDeHF2af+8Fn9ww7b3XWh66syfDoBAAB6VYas9JXER74IIVTnV58dPptvPnKl8wnj43OLiw936vXDw2fz1WoIYXf9xsTMwmat83kAAADApbp+V/HnM5UfH0+qV6vz09Nh77jKXePHrq69/3BxPOhCl7MyfM8EAADQqzJkpQSr6//r/2H9+UGGlzib23Why0kZPp0AAAC9KkNWSvQOa5sL79xIXK3+PDPwfVGGTycAAECvypCVeutCNxFqIRw+mDipZv/+RPeXGB9X464PyvDpBAAA6FUZstIr3Q44fLq+uxt2d3fnbz4M42E8hH/7cfOpj381brIdAAAABip57foT33yjeeeNb+Y6FAAAAKCr5El+77Nm97ivH3efu/L1/McDAAAAdNJ1df3EtWoIuyGE3TsTM48bXeiaT+3dX1h42v0ljrvQAQAAAJkl6EI39d+vH7zI8BKTy/X9pQzn01YZqjgAAAD0qgxZqeucfAiZYvzQ2r499d5+pitMfbD/ZDan0QAAAEBCCZJ8tVoNIYTpuzsPJ2q1EP7tfzdx7yCEEK5Ofu8bv9v9/B/8INsQ+2Nn/+DgIOMlQpDkAQAAGLAUqw42FyrH/eTrEXeh2749dWvj4Cj9BQreNVCGFSMAAAC9KkNWSvEOa7XNw8MQQpiYmBuPu5Td9u0r1zeOQghhbHJ544OZnk6enS10Rr4Mn04AAIBelSErjf477OIkzI/d2noZ0773Mnw6AQAAelWGrJTHO6zVap2eHh/2ifuVqcq9gxBbli/DpxMAAKBXZchKCbrQzdzfC6FR8W7u9JG//5vfHP7Vi6ME+8wj6EIXY5Yvw6cTAACgV2XISglq1+/u7oYQwvSFR0bH0v7yh5V7B+Fo472VMOxfOwAAAFBqybvQnXr5nbHw+elk/NjY1a9+tcP5r34z3dAGaumD5Q/f+zCEELYH3luuUqkM9gUBAACIWJra9WszE3cak/LV1cOdxSHfBT+qyrBiBAAAoFdlyEpf6f2Uw+fNtfXV1UdiPAAAAAxUiiR/Yvp1OR4AAAAGK8E++fMmrlVDaC15F3sXukttb6/s7IQQwszM0mwkJe0BAAAYcWn2D2wuVG6shxDGvhOOPu9++PyzeqN9XXSOm9MNZSO9Muz9AAAA6FUZslKa1fVz7//x74UQEsV4AAAAIE8pVteH2kd/8ZctP177/vw//ScdDr82keI1AAAAgHZSJPmfv/Mnrbvkw/Nfrz//dZu28ycOQ4h1pzwAAAAMmRRJ/osvj9o9vLu72+7hEKZ7fwkAAACgvTSr649dnax+99XcRgIAAAB0lyLJ/4t/Vb13ZzeE8KN/sxNpUXoAAACIVYra9eOvN9fL733WsY88AAAAkLtUffZqazMTd3ZDzK3i41eGHokAAAC9KkNWStNPPowvPlqthhDC+o2ZhbVNM/MAAAAwKF2/q9hcmLm/d+aRL3/zH774/0I4Ojpbwn5sbCyE8NWvfvWr/+i1f/i13/mdkyem79pO3wdl+J4JAACgV2XISgkq3l3aXu6sRrI/OjoKL1583vqELnQAAACQmwRJvlqtnvm5OSd/zvkp+hBCuHqt+t2vpR4aAAAAcEHeqw5qtc0H79xfP57GVxKvb8qwYgQAAKBXZchK/XmHJ8XtZfm+KcOnEwAAoFdlyEqpatd3Nb54d755d/3pZl9eAgAAAEqpP0k+hLmbx1F+7zNd6gAAACAvXSveXexC19H09PS1m++/OTc+ca0awm4IYff5YQjjGYYIAAAAnMivC93pwevrd0J1fv4fN5I8AAAAkJ8UXejaO5f3d9fXxXgAAADIXZ+70IUQqquHO4tW1+euDPUYAQAAelWGrJR3xbvx8bmHOzuHq6fT+F/m/AoAAABQZn3qQvfm9NXj+6+OmZAHAACAvPQjydc2F95Zf3H8098f6UIHAAAAeUlQ8a5WSxbFDw8Pw2efPX1852ytu1/rQgcAAAC5SdBPfuLGeqpLXw3hRfejAAAAgB70Z598tTr/7Oc/6sulAQAAoNS6zslPXJufn+96mWs3b77eOHxiYnx8PIRQW5tpPFW9NpFphAAAAMCprkl+fPHhwzQXPny+2/0gAAAAoDf9WV0famv3m5vrq2+9qdwdAAAA5KVfXejuNGfkBXkAAADIU8YudL/95f/8Zz979h8/+eSTk4fGQjg6vl9dfbQoyAMAAEB+KvV6veMBmwuVtF3o5n7+75/9kSDfJ5VK198dAABA6ZQhK/Vpn3wIIbzY/PGDzf5dHgAAAMqo63cVtbWFB8/PP/hXH69vHjTuXp2c+4Mffuu/belCFw4fvHNjvblPfv5Z/eFcvkMmhFCO75kAAAB6VYaslOYd1tZmJhoV7aqrhzttN8InOIRsyvDpBAAA6FUZslKK1fW1jx4fT7jfvSyjjy/enW/c23380eUF8wAAAIDepEjyh8+Pg/zNDuvm524eR/nnh72/BgAAANBWxop3tc21hZmZmUqLmZmZhbVN8/AAAADQDyn2D5z0pbv6nfDi80sP+87V8PmLEBS965My7P0AAADoVRmyUoo5+ZN1860xvtp0+kgjxodQvTaRfngAAADAGWlW18+17o///vyzw3q9vtNUr9cPn81///T5ybfeVLkeAAAA8pImydc+e3H6w6/3nh7WWnbF12qHT/d+ffrzV1MPDQAAALggxf6B017xiWgo3x9l2PsBAADQqzJkpSxd6ObmqpcfVZ1rLsHXhQ4AAADy80qGc7/1r3fqz2q1zY8ePH2+t7cXQghhenr62s3335wbH99cqGzmM0YAAADgWJYkv/dZLcyNj88ttmsyV/tsL8OlAQAAgLaydKHbffxR7bKDah89bq7B14UOAAAA8pOqEsDmQuXGegihWc4u1M4H+t8++ufX7zcK2H//7uH/9acK3uWvDFUcAAAAelWGrJTuHfZUvn7+Wb3d8nuyKcOnEwAAoFdlyEpp+smHEMLf5ToKAAAAIJlUFe82H9z5pNsxVyfn/uCH37oSQrBPHgAAAHKTIsnX1u6vN+9WVw8fvXnYvgtdfmMEAAAAjqXYP3BS7666erizKLEXpAx7PwAAAHpVhqyUdp98CCFMvy7GAwAAwGClWF0/ca0aQmvh+tqFLnRnjFtpDwAAAHlJs+rgpAfd1RBedD9cF7q+KMOKEQAAgF6VISulWV0/vvhH1RBCohgPAAAA5CldF7r/s3Vx/bXvz//Tf9LhaF3oAAAAIDddk/zmwsz9vTOP/N1f/4cz3eSf/3r9+a9DqFarl1ziMAQ75QEAACAXCebkd3d3ux/U4bDpXsYDAAAAdJIgyZ+fbP/yN7sHL0II4epk9buv9mVUAAAAQHspavqdlK5XlL5IZajHCAAA0KsyZKUUtevHp6e/E0IIYf3pZs6jAQAAADpLkeRre3ufN+6t312r5TscAAAAoKMUSf7w+Ulpu1/fmZhZ25TmAQAAYFC67h+42IXub36z+/zFxQMv7UI3fXfHdvr8lWHvBwAAQK/KkJV0oQMAAICYpOhCF0L4+7/5zeHzF0chjF39zrde+/rXfqcfQwMAACAqlcqZH0d9arwwqbrQLTx4HkLYW19vnYW3un6wyrBiBAAAiEilcj66X3xkIMMY/ayUYE7+vMP/fX39FxcftroeAACgrNqG9nq9mDA/8lIk+b/+v8dCOAohXJ383ndf/d3ch1SM7e3tEEKYnZ3tduDtqff2Qwhh6oP9J90OBgAAGH0d4row3w8pkvw3po/Cbggh/Ojf/Dr+ZfPbK7ff++nGwdHpI2OTt37ywZOly0L6zv7BwUHjXgiSPAAAAAOWop/8CNm+feX6vTMxPoRwdLBx73rlyu3tggYFAAAQka5T7o1peXKUIsnP3Zxv3Fl/upnvYAZsZer6xkmIH5tsGGv+fLRx/crUSkEjAwAAgMukmZOfe3j4bL4aQli/MbOwtlnLe0yDsX37pwfNu2O3tuov9xte1reWbzXi/NHBvYowDwAAwHDpWp3/uOdcuPb+w8Xx1ke6dKH7m9/sPn8RQgiTy/X9pTzHnIvt21eaM/Jjt7Zeni9dt70ydf1eI+iff3plqtJ4puD3VYbOCgAAQBQ6L7AfcMW7MmSlrhXvDp+vr6+HEML8zYdh/MwjZ13ahW447ew3F9aPXX/3Yt262aX9rdAI80cb16dWhvG7CAAAAEopRe36k+n3k1n3q9eq3/3a+YNOnh1yr73RvgD97NL+1qeNefuDe1duz1yYtwcAACCEjq3mtKDrhxRJfu7hTqP33OZC5cZ6CCH86Kc7F9vRnTz7wx9kGmGBZp+8XG6spT/auHV7W5YHAABor22YF+P7pLRd6GammlXqv/i0U7u5pf3lyRBCc5F9/4cFAAAQqUaYb72J8X1S2iQ/++71ZoX6jfc6JvSl/a1mLfuDe5rMAwAAXK5eP3OjT0qb5E+jfDi4d+X2SoeIPvvkZTPMH21cv3LSuw4AAAAK0DXJ//Ve887eX/d25V993Lzz8a96O3FQZp9sNCfbw9HGvesdW8e3hPmj3AdSSSX3YQAAABCFrkn+iy+bd7784vxTqUP+sJh98nLr1uRY8oOXkx7ck3oqfRgIAAAAEciyur5DyI/G7JP9l/WtreVbk5NTM10PXtp/Wd9aThz+AQAA4nKuZB3DKVU/+VEzO7s0u7+U9OClJ4mPBQAAiIc2crGQ5DvY3l7Z2QkhhJmZpVm95AEAgBHWNrS37RJP4ST5Dnbeu3fvIIQQJpeX9iV5AABgVHWI68L8EOolyddqtRRPAQAAAPlJnuQP7k1M3Ov5KQAAAIZa1yl30/LDJkvtegAAAGDQus7Jf/PV5p3JufkffuvMU3/18frmQfunWp999ZvZhwkAAACEEBIk+a9Ph7AbQgg//NcPH86deWpzoZnVLz7V+uz013MZKQAAAN2cawKfZEl818XzltYPG7XrAQAARoSG8CVhnzwAAMAo6NAQvqsOh/kuYAil60L329/+8i//4vP/9ePmjx//T2+//b989/r1P/i93//2t3MeYJGW9utLRY8BAACgu+wN4dseJsYPp0q9y69lc6FyYz3TS8w/q1/cRU9WlUrX3x0AAFAWeW10T7HNftiUISvZJw8AABC3HBvCj3oEHhFdk/zEtfn5+fBy79/9YvdFy8NXr07+w+9+5zv/4Pjn//T551/+vwcHrYeEq9U//NH0lXBtIsfxAgAAQLklWnVwZoV9dfXZo8W58UsOrW2uvXPjzu7xj1bW900ZVowAAABJJJlvL8+O9zJkpQTvsLY2M9HM5tXVw53Fy0J8ljPoWRk+nQAAUELpdqprCH+iDFmpexe62kePm1Ps1dVHyUL5+OKj1Wrj7u7jj2qdDwYAAKChEblbb0l6yFE2XZP8aZCfv5t8cn188e58497u88N0IwMAAIhOpXLm1uu5GsKTRPc5+WPV3irXTVxrzsrvfWZSHgAAKIMsM+pdG9wdDGMAACAASURBVMJ31fYwMX4kda1d/8vjKfkv/7cHC897uPJffdn4393Hvwx2ygMAACOuw4z6wLL0xTAvxo+krkn+i2YgDweb6wepXuLLL1KdBgAAEIuuM+qdE7WG8PQk+ep6AAAAoHhd5+R/8MMQDkII4Q//7PBPf7+HK//yTyb+5S9CCOGHP0g5NgAAgAjkOKMOSXRN8ieufGN8vJft7odXeh8NAABACXWN+r4IoJXV9QAAABCT5HPyIdRq+skBAACjLUXt91xm1DtcxIQ85yRP8us3Jtb7OBAAAICiXczMg+8hV+AAiEXX1fW/+jjrS3z8q6xXAAAA6LsODeG76nBYT1G8cZ3WmxjPRV3n5L/5ataXePWbWa8AAADQXxkbwl92WIooLrrTVdck//XparXXi+7u7rb8NP31Xs8HAACI0MWZebGcfqjUc/5k1TYX3rmxfpLkq/PPHj2c66V7HclUKrn/7gAAoKSSzJxb6B6LMmSlXLvQ1dYWZiZOY3x19dnhjhgPAAAAOeqlC10npuIBAABgELquOthcmLm/1/kaf/flb2oHL46Ofxy7Ojn+3Vd/9+Tp6bs7D+eyjZKLyrBiBAAABiZ7Q3iGRBmyUoI5+bP167o7enHwyYuWn6d7GxEAAEAGas4x8hIk+eolxesvn4rvNfsDAADkInUfuA6t5kzIM2zSrTqoba69c+NOy6741bvvLza2xdswPyBlWDECAAA9yR7Fc2kIT7HKkJV6r3jXIarX1hbeudPy1OqzR4tSPAAAMAAdIneH+fa2R557BIZNb0n+8qhuKh4AABgFojvDL3GS7zQVL8UDAABF6jrlnnxaHobfV5IcVFtbmJk4zerV1WeHO42sXttcm6mcPlWdXz2s74jxAABAepXKmRtwTtdKALW1mYnT2nahuvrs0ZsTIYQQfvvLP3n/X/7ik+NnvveHf/bgT3//2xevMD4u2PdBGao4AABQQulqzuV1DCOgDFmp6zvcXKjcWM/0EvPP6g/nMl2BNsrw6QQAoGyyFJ/vfIwYXx5lyEqJVtcDAAD0W9fi80BD14p3E9fm5+ePf3i59/Ff7B68OP7xanXuD6a/daXLFa5NZBgfAAAwYBnbsBXVxa1DTTsT8oyYxKsOFKgfMmVYMQIAQDpZsnS6berZT+/fZngxvmzKkJUy1q4HAACGSyO4tt6Sr0tvG3qTXyHj6blovFzrbdQzHWWUoXZ9UmrX90UZvmcCAKBXBVaM6+vpyY+BMmSlru9wZapy7yDTS5ypXV/bXHjnRrirmn1mZfh0AgDQk2GO4orPMzBlyEqDq11fq20uzFRaFukDAADDomtO7rxIPuPpQE+61q7/F/9qfv/xv/vFbqNg/dXJ6vff6F6u/oxr/9nm2sL9O80EX1093Fm03B4AAPKVMEsP81Sl4vOQUNJVBxdK16++dfPNN+cu3wJfq9UOP3pw//H6rnr3fVGGFSMAACSXcfl6sad3PkyMpydlyEo9vcNzcf5YtVoNIUxPT4e9vb0Qwu7uxUOE+LyV4dMJAEBy/d6IPoB98q0Ht/JnLz0pQ1ZK8Q5rmwvv3F+/mNbbqs6v3n1/UYbPXxk+nQAA9CT2ineQizJkpa7vcHOhcj+0nVCvba599PTx470Lc/DVanV6+q1rN99sk+DVrs9LGT6dAACllW5Sun/V41MvjO/pdMhFGbJSkiR/Yz001se/32FffFe12uaD5tr8M33pSKcMn04AgHLKslE8e5bOuE3dLncKV4as1LUL3dzD+uFqNYTd9RsTE5WZhbXNWq+vUdtcW5ipTDQa0FVXD8V4AAC4RNvcm7yFW9sje8rSjSu03nrKRBlPB5Loc+36P360/sknpycpe5efMnzPBAAQqdQF2/Laaq5iHGVWhqykdn2syvDpBACIUT/Wxvd6HSizMmSlFO/wz29UfrzZw/FzP68/+6MeX4OuyvDpBACITpZt6jm2ZIcyK0NWeiXBMbXama3xX/9W887c/B//g189+4/hk9MF9CGEEL73ve/9V//l7/4fm7ufhxBC+NbX8xgoAAAMuQ4xu7F7fNTDBTAgCb6rqK3NTNxJ1j2+nerq4c6idfW5K8P3TAAAcelrP/bkx0DJlSErda1dH8L44qPVatrrV1cfifEAAIy+rhm7a/35rgeI8UBDwu8qNtcWnj5v3t/bW2+UtKtW56en2x5+7ebN10MIYWJiIoQwnqELPZcpw/dMAAARyWVGXcU7yK4MWSnFO1yZqtw7CCGEyeX6/tKlhx0vyre6vj/K8OkEAIhIv2vaifGQUBmyUoLV9ee9dnzn1dc6HXb4vLG3fvf5Ye+vAQAABapUztySyGttfNvriPFAqxS168Orzf/98ovtWu3b7c85fHB/PdPAAAAgvXNhuKcYnKUhfC4uhnkxHmildn2syrBiBAAgnSxRPOPidmvjoXBlyEpq1wMAMFLaZuauS987nNvTFayNBwYgTe36j9d3D0IIIVydm//Rt9odflK7fm5OjO+TMnzPBADQq752dO9pYr+Vv9pgkMqQlVK8w82Fyo3jPfDV+dW77y+K6wUow6cTAKBXWaJ4XsXngWKVISuleIfbM5Xru+Hq5NUXBy9aHq5WL1mCP3135+Fc2vFxmTJ8OgGAMksxrZ0xikvyMBrKkJWS1K4/57chhBDOxvgQwu7uJVXxpnt/CQAASq3w6vEAwyxFkv9/vmzeuXqt+t2v5ToaAABGRuq94h1K1vU1zHd9Cd8mAEMiRZL/wQ9DOAghhB/9dMSXzW9vr/zsvZ9ufdH46bXrP/ng3aXZ2WLHBAAQhdST6l2rx3e4iCgOlESCLnTnzd2cb9xZf7qZ72CKsb29cntqampq6vbKdsujt69Url+/t3FwdOxg497165UrU61HAQCMqkrlzK3Xc1P3gStWh0H6FgAYHukqAdQ2F965sb4bf+367dtXrm8ctTwwdmvr5ZPZsDJVuXdw6VnNg4pVhioOAEBRsmxTL7x6/GUHZHkLYjxEpAxZKcU7rK0tPHgeQthbX29X425sbOyr/+i1b3zj1d9tPjC0tesvxPiGyeXlcK+R48cmlzf2lxqZfXvl9q17x4cPQZYvw6cTAChExiRceJJve0yvUVxDeIhXGbJSxn7yScw/qw9lkj+ddx+bXN74YCaEnfeut8zEt0vrp+dMLtf3lwY21jbK8OkEALJIl0UzJu3h6QMnikNplSErpdgnH0K1Wp28evahsaazj16dvLTLfOFWPmyG9rFbG/tLs7Ozs7NL+8uTJ89P/qTNpPvpEQcfrgxilAAAqTTibutt+PeohwR76ZNPrZ97+wCjJE3Fu4c7d6dPuslX558d1uv1l031ev3w2fxxen9xMLxL6z9tlqQfu/7uaWJf+uBW88uIybfbz7jPTDUPEOUBgGGVuuBc15wcyzcCAKMtzZx8be1+c3V9dfVw5+H5enfjcw93DlebYX79/lot0wD7ZWe/ueX9tTdap95n33it83ldDwAAKFTXLm59lX1SXfV4gK5SJPnaR4+ble7m7y5eUrV+fPFus1Xd7uOPhjPKd/HFp5rNAQAUom2YF+MBTqRI8ofPj4P8zbna5trCzMxMpcXMzMzC2mbtpOv87vPD/Iabn8tWyS/t1+v1er1+WWn60+31UzN9HSAAQO8yLo/PZZt6LpPqjYu03sR4gBNZatdPToaDy5uunzw7pLXrW3rQJa9Df3pS4X3oylCPEQBil7F8eorTs9d+z94l7rIjpXFgMMqQlVLVrm9qjfHVpvbPDqPZJxvH1e0O7lWuXJla6bycfnvl9tRp//m2le0BAE5lrB5fVPH5vLapm1QH6J80teuP182HEE5q1+80na1dH0II1WsTWQfZJ7NPXi5PNsP80dHBhzudDl55797GQTPGj93ayrOXfCWV/F4fAGjvXBDt9dx01eMznt6/5fEporg+cAB9kmZOfiKcNJP/zt1H7WrXP7r7neOfxq5OX1IVbxgs7b/cWr51HOeTGJtczntZfT2VPEcAACMqexRPNyWesXp8scXnW1/IjDrAcEpVu37vuJl8+Pz+xMzCZq2lOn2ttrkwM3H/8+Ofj17sDXft+tmlJ/sv6/V6l63yM2/fWl7eqtdf7i9ZVg8AMcg9isfSSj3H5fFm1AGGU5aKdwkNacW72JWhigMApK4Yd1lk7XdBuOwvkX2Elx1jXh0oiTJkpSwV7+bmqpc/WZ2LP71vb680bOstDwCDl3pSfRhWpxfO8niAEfZKhnP/0z97VH8WapsfPXj6fG9vL4QQwvT09LWb7785Nx7WZiY28xljYXbeu3fvIIQQJpeX9q2pB6CEMjZRy3KFDuvb+5pIE/ZjjyIVRzFIAFJIkeTnbs6H9fUQwu7jj2qLi+Nzi20Wz9fWHu827g1v7XoAoJPsy7NTX6HrpHqW1e/9juIZR5j9DQIw8tKsrj9pQ7d75521tuXsamvv3DkO8m+9OcS16wGA9rKXfIu6aBwADLNU++Tn3l9t7pDfvXOudn3tz/985cbUxEmOX320KMgDQGSy7zPPcoWEk+p90r9+7AM7HYCRl26f/Pjio9XHzbi+u35j4pJS9r/3x3I8ABQq+0b36AzJ6vS2w0j+0hlPB2C0paxdX/voeBt8J3/5Pz6IvegdAEQsXe337FPixU6qZ5djP/Ys1eMVnwfgMqmS/Ok2+Plnh4fPVufn57/3e2PNJ6/eWt76+fHq+/UbC7I8ABQh3m3qff2mIGEebnuFFFn63Dcpvcp4OgCjKk2SP56Qr64+e39ufHxu8eHDmz/4y6PQeOzfP1ma/aPFnWfNqnjrT0V5ABg0DdWzR3FT4gAMrRRJ/jjIz99dnGvugq99ttd8cvr15kMT15rT8nuftS1vH4Ol/XrD/lLRQwEgXufS4IBPT2EAi+cHMKke8ojipsQBGE4pKt4dPm/MyJ/2iT/dNT//34TNzc0QQph4fTqE3RDC7vPDENS9AyBSGSvGZSxalu70whuq5yKXkm9D/h4BIJ10tetDCGF67HBt4aM3Hy6Onwb5sfUf3zipY3818+AAILssUTz3HB56SdEZT8+iw6v0tM88yxVCu5l5yRwAQpYkv/7jGyHMv/4wjDcn6UMIR60HvMgyLgDIQ5Yo3o8cnvwiGU/PLvuUuEl1AOiTFPvkJ659/8zPm0/PtJOvrj47fHZcuz6EcO10FT4ADFKW4u1RV4zLvk299ToZ95krGgcAuUuR5Menv93oODd2a/mtidra/dYgX119tDg3PvfmW9eOH/naf26TPABZpCv5VmwUz1gTbnj6sWcv+aZoHADkLsXq+tpes+Pc0ca96xv3zj45/fp42Fyo3GhJ939bU/EOgLSyL8/O5UXPGf6KcblsUwcAhlOKOfnD55+EEMJYu+fmb86df2j3+WHvrwEAIcPy+OGZ0y5Q9obqAMBwSl/x7u0/O7z5tw+ePg/hvwi/ur/+SQgtnemq1fl/9o/X7/0ilzECUEqFl3zLousIOz+b8fRz1zn3CAAQu/RJfu9vw8PFh3MhhM2F5h8J1bfeHA8hzD2sz4Xa2sx6p9MBYGjlFaSHQSzjBACSS1W7vhpCy6r509r106+f7oc/aU1XVbsegJ5lXB6fV/H2LDqMIcmrZzwdABhhaWrXv/lWNYQQ1u+vbdZqLbXrWzbJnz7anKcHgKjkEqQz7lS30R0AaKtST/HnQG1tZuLO7rkHq6uHO4vjIYQztevnn9UfXiiCRw4qlVS/O4BIJMmrXY/JXrw9l8r5GXeq2+gOAD0pQ1ZKMScfwvjizrP56pmHqquPFi/MvVdXD8V4ANLIZXl89jntxhVabyn+MMjYUF0/dgDgnAzfVdRqmx89ePo8hGs331+ca4nxmwuV+3vzdx89nLOuvn/K8D0TUHJ51Zwzpw0ApVKGrDT673BUleHTCZB9eTwAUDZlyEqpVtcDwEAo+QYAcFH6fvIAMAAXw7wYDwCUnCQPwLAT3QEAWlldDwAAADGR5AEAACAmkjwAAADERJIHAACAmEjyAAAAEBO16wHoO23kAAByJMkD0F+VyvnofvERAACSs7oegD5qG9rr9fOz9AAAJCfJA9AvHebehXkAgNQkeQAAAIiJJA9AX3TdDG9aHgAgHUkeAAAAYiLJAwAAQEwkeQD6ouvieb3oAADSkeQBAAAgJpI8AP3SYVrehDwAQGqSPAB91DbMi/EAAFm8UvQAABh256J4ryH8YpgX4wEAspDkAejk4vx5ihl10R0AIEdW1wNwqbahvWtRegAA+kqSB6C9DnPvwjwAQIGsrgcYfbapAwCMEkkeIAJZoni6je5dj2lMy/tSAABg8CR5gEEYfBTvcKQQDgAQNUkeoO+KiuJdN7oL8wAAMVLxDqC/spR/L7DmXNfr+yIAAKAokjxAHxUYxRNudAcAIDqSPMCQKjyKd7i+CXkAgAJJ8gD9UngUz67tCMV4AIBiqXgHMJq61rRLGMgvhnkxHgCgWJI8wJDKK4rnMhIAAIaHJA+QSIp56cKjeIcBWCEPABAvSR6guywN4bPIHsXbXkGMBwCImiQP0EWHhvBd8/AwRHEb3QEARowkD9BJ14bw6cL8gKO46A4AMEokeYC+E8UBAMiRJA9wqYQN4RMukgcAgFx8pegBAAAAAD2Q5AEAACAmVtcDcci4zzzd6YU3hAcAgIskeSACGWu/a6gOAMAosboeGHYd2rkP4PQOR/o6AACAQkjywIBUKmduyc/q3M69r6d3OFKMBwCgKFbXA0ll2ake+/r27A3hAQAgL+bku1qZutIwtVL0UKBAjeDdess4r55xRj3JRTKefvHg1hsAABTFnHwCR0dHRQ8BitUhinfNtF3Xt0vFAADQE3PyQBe5bDUHAADyUqmXdDpsZerKT79IdGTLjPzY2Njp46/95OX+Uu7jSqxSKe3vjkHL0lA946R99uvrBg8AUDZlyEolXl2fYs28ZfaUT8Kt5qP+n0oAABgipV1dPzM11v0goHAZ27nrBg8AwOgpbZKfffKyvnVr8jjOj91a3qq3tzzZPGZy+czjRS6thxTStXPPqOtG+tRpPHkO1w0eAIARU9okH0IIs0/2X24tT46FEI427l2/MrWyXfSQoE9S95DLJYpn1xhG662nF814OgAADJVSJ/kQQphdOk3zB9I8oyl1O/dc5LW+PWM7d93gAQAYGaVP8iFI84y27D3kskdx69sBACBHknxTI83fOk3zt6V5OJE9ilvfDgAAeZHkW8wuPTlN8xvXK1dum5wncgl7yCWRPYpb3w4AALmo1P1BfdH27SvXNxqt48cmJ187ODgIIYTJ5f7Uq6+k3azsd0dXSfK26XEAAEZJpTL6OdecfDstLeqOmjG+jy7pftdFnwcFAADAkJLkL9PSog6iNSQ95AAAgBy9UvQAhtrs0v7LmZXb7324H0IIUzNFjwcAAABGf/9ABtvbKzs7IYQwM7M0O1v0aM4pw94P8nLZxLsJeQAARk8ZstLov8MMVqYq9/pa6y6LMnw6OefcOvmefv8XQ7sYDwDASCpDVrK6HuKQMYpf3DA/6v9xAwCAkSXJQwTahvZGOO8pzAMAACNA7XoYdh3ietfS9AAAwOiR5AEAACAmkjwMta7r503LAwBA2UjyAAAAEBNJHgAAAGIy+n32RlUZeiTS0HmBvbbwAADQqgxZSRc6GBwd3QEAgOwkeRiQi5PnCafTO/SNNyEPAAAlZJ88DELbyJ287HzbI8V4AAAoJ3Py0HcdIneH+fa2R557BAAAKCFJHqIhugMAAMHqeui3rlPuydfYAwAABEkeAAAA4iLJAwAAQEwkeeivrovnlaAHAAB6IskDAABATCR56LsO0/Im5AEAgF5J8jAIbcO8GA8AAKSgnzz04Fwa7ymHXwzzYjwAAJCCJE+JZAzSF6fQe51UF90BAIDsJHnKImMOb3twY5pdPgcAAAbJPnlKoUMOT316rxcBAADIhSTP6JPDAQCAUSLJQxdd18/7OgAAABgkSZ4RJ4cDAAAjRpIHAACAmKhdT0wK6cfetUC98vUAAMAgSfJEI10bOTkcAAAYMVbXE4eMbeQy6vBCvggAAAAGTJJnoCqVM7fkZ2VpI5dLDm97ETEeAAAYPKvrGZx0y+Nz0XaNfa+vfjHMi/EAAMDgSfIMSIfl8Z3zcMI2cgk3zJ97pFeiOwAAUDhJnkHoujx+YDPzAAAAsbNPHgAAAGIiydN3CZfHp3s2yfUBAABGiSQPAAAAMZHkiYB27gAAACckefoul+Xx2rkDAAA0qF1PNLRzBwAACJI8g9Gh1VxP8+qiOwAAgNX1DIjl8QAAALkwJ8/gWB4PAACQnSTPQInuAAAAGVldDwAAADGR5AEAACAmkjwAAADERJIHAACAmEjyAAAAEBNJHgAAAGIiyQMAAEBMJHkAAACIiSQPAAAAMZHkAQAAICaSPAAAAMREkgcAAICYSPIAAAAQE0keAAAAYiLJAwAAQEwkeQAAAIiJJA8AAAAxkeQBAAAgJq8UPQAiU6mc+bFeL2gcAAAAZSXJ04NK5Xx0v/gIAAAAfWV1PUm1De31+vlZegAAAPpKkieRDnPvwjwAAMAgSfIAAAAQE0me7rpuhjctDwAAMDCSPAAAAMREkgcAAICYSPKX2d5euT01deXY1NTtle3togdVkK6L5/WiAwAAGJhKvaQJbPv21Hv7IYQw9cH+k9kLT165vnHU7rSxyVsbF48vQqUy0N9d56wuyQMAAENiwFmpEKWdk9/ZP2jY3zn3zMpU5ZIYH0I4Oti4fmVqpd+jGz4dpuXFeAAAgEEqbZK/zMrUvYPm3bHJ5a2t+rGt5cmxxuNHB/eu3C7hQvu2YV6MBwAAGDBJ/ozt2z9t5vixW1sv95dmT9fRzy7tv9y6dRzmN94r4bz8cZhvvYnxAAAAAybJt9r+2VZzWf3kT9pthp99snGc5Q8+LGWUD6FeP3MDAABgwCT5Vjv7x0H+7aX2R8y+e73sUR4AAIBCSfI9mn3jtaKHAAAAQJlJ8q1mpsaKHgIAAAB0JMm3mn3yk8kQQghffHpZbfqVD49L4k3NDGZQAAAA0EKSP7hXqVSuXJmaun17ZXt75oPlyRDC0dbP2kb5ltr2199tUxIPAAAA+qxSL2n98ZWpyknj+LYml+v7rWXvtrdX3rt17+Co/bODV6mU9ncHAABwqTJkpdLOyS/t1+tbW1vLt25NTo4l2B2/8t71kxg/NrmcZ4yvpJLf6wMAABCT0ib5EEKYnZ1devJkf//ly3q9Xq9vbS13D/Zjk7e2XuY7HV9PJc8RAAAAEI/RX3WQk+2V2zvh3aWlodkcX4YVIwAAAL0qQ1Ya/Xc4qsrw6QQAAOhVGbLSK0UPYJhtb6/s7IQQwszM0uzQTMYDAABQaqP/XUUGJ/Xti69Uf1EZvmcCAADoVRmyUqkr3gEAAEB0JHkAAACIiSQPAAAAMZHkAQAAICaSPAAAAMREkgcAAICYSPIAAAAQk9HvszeqytAjEQAAoFdlyErm5AEAACAmkjwAAADERJIHAACAmEjyAAAAEBNJHgAAAGIiyQMAAEBMJHkAAACIyStFD4D0KpVK0UMAAABg0Cr1er3oMTBolYrfO4Xx8aMoPnsUyMePovjsURSfvX6zuh4AAABiIskDAABATCR5AAAAiIkkDwAAADGR5IH/v707xk7cCsMAKhYgNpANiC79lLAB6LKGTDk1HKinzKwhndmAKKdPBxvIBtACSAESAiTAY2Hnx/dWc4xkOycfMp/e03sAAEAkmjwAAABEoskDAABAJJo8AAAARKLJAwAAQCSaPAAAAESiyQMAAEAkmjwAAABEoskDAABAJJo8AAAARKLJAwAAQCSaPAAAAESiyQMAAEAkvd1u99G/AwAAAHAvY/IAAAAQiSYPAAAAkWjyAAAAEIkmDwAAAJFo8gAAABCJJg8AAACRaPIAAAAQiSYPAAAAkWjyAAAAEIkmDwAAAJFo8gAAABCJJg8AAACRaPIAAAAQiSYPAAAAkWjyAAAAEIkmDwAAAJFo8gAAABCJJg8AAACRaPIAAAAQiSYPAAAAkWjyAAAAEIkmDwAAAJFo8gAAABCJJg8AAACRaPKfxWoxGfT7vVK/P5gsVh/9S/HMFoNer9frT27ETDLpwD5GxxzdFSTZoyO/EiXx4wFWk32mBotrB8keb1QGrU3bZz/Z696O55fPs7Tx/36azfOP/uV4TvPskLHxlYhJJh3Ix80pOiSp5STZoxutUbqSJfHjIco/vEnSduWTPTpxjFrL1a/hs5/sPYQx+ee3GIxmm6LxpWIzG129cQu/YjHozzZ3HCWZvNVq0h8tm1OUJElSbGZNQwOyR0euRKk1S+LHQywGN//wyh6dWP3z72tPkb0H0eSf3Wryvbyyp+Pqplftxtjm+63pz/AKq8Wg3/rJtn6cZPJmq8m4rPFpNs+Pd/XzeTVQXyzHZ0mSPTpyrE5pNj7m72qWxI+HuKPHyx4d+bne/+VtnfuxfRmenCB7j/P2YX3+z6r5L5cTXY5TUlvfifAa+Xx8MXWqbXa9ZPJ2VVSaY9YSMtmjI1WUGuJSZensNfHjEc4nOzdFSPboSJmXq89P1sne4xiTf26Lvw/3wLJvZ7fHkmT4sjy8fTZ/m9TCG60m/f5ottwPxqfZ/MYzVJJJB6phgcsUJUmSTP86BKlY/zx+VfboSBmldPzX9OLF4e+/7f/x7z+rhnPEj+6sJvsH2tLx/MqqIbJHR1Y/8v1nvdGfTX96L8neA2nyT616kCX74/JzRpIM/xx599CNn+viUOLH83y7bspbjWTShel6f0u6LW9VmaqRPbpS5u98HmmSJLWaf/JZV/zoXPmQUTpevny5cpjs0ZHyJvpvv99X5GXvkTT5p1aNWDW+d5o/58IvSrN5nm/XL9Pbl3bJ5D00LcojezzYarWYVIt+ng1BiR8dK3t8Nm+8ud4cVgAACUlJREFUo3Qke3Sk/MuaDr4kq0VtU7m2PeVk75E0+Wd2e23JL4P9fbDT6X/watP1brueDl95f7aVZPJ2i6/Li48PssfDLAa9Xq/XGx2eM0qzcX42X0T86NZiMDr0+LtnwrWSPe5TFvMkH/dGs01RLXFcFJvlbHSxl7zsPZQm/xmkgysTruDDSCaPU63k3PgUs+zRtYaPqz9bPpaKH10oL3K3e/yR7PFG1UPvRdGyqdxy1LT7q+w9hib/zKrbZjedLAgFDyaZPFi5AtT+2dHaVBHZ44HSNM2yND0stLhZzkb9k12SxY/uvK7Hyx7dON6yTLPxyeavtT3lTnZ/lb2H0uQBeCarSX90mFd/1uPhcYYv2+12u15vt9vdLj9s31FsZo2jU/A2vzIeD283fNkeqvt2/VJ/pnI4nK635ZUvKfIfLnzvQpN/ZuWDJ7eZ8sJ7kkweZbUY1Gp8frEGlOzxLobTdblNcrH8Wo7Lix+dOG47l9/b42WP9zA87v5aVXnZeyhN/jMwXYX/J8mkS6vFoD+abQ6r3M0va3yN7PFow5dvh9Gpi2WcxI83qG879+opR7LHY1V7yl1ETfYeQpN/Zrf3dXjtnpDQBcmkc6vJscWn43y3bt4NUfZ4P+VQVPUBVvx4u9WPfB+SYjnqnSknJCWb2WFfsPLZDtnjo8jeQ2nyT+3Wvg71PSHh/UgmnapPqb8xGC97vLtjmMSPjyJ7vI+ylrvuvQ9N/qmV98FaFp6obuy6C8b7kky6sxj0DoPxaTbPty2D8SXZoyOrSX8/7HmyPH39gDJMR+LHR5E9unDzuldtUndMkuw91I6nVi4imaTj/OylcjWeJMnmH/K78czK5F0G7/R1yeRNjmlpi9oF2aMbV5K0a42m+PFAVYaaIiR7dOD6da969TRJsvc4mvyzO75FkjSbl2+g2qaP93/+hfvdavKSSRdu5qyJ7NGNsyRVocnn42OYzj+eih+Pc7XJyx5duOu6d54k2XuY3m63S3hqi0Fvtml/OZvvbEZK58rYNW0EdnZIC8nkltrG8TecpUn26MbNCDZdAcWPR6kC2ZIi2aMDN2LkuveuPCf//Kbr+k2vE2k2v3svUuiYZPI2DY8h30n26MbwZVsbazrXciNT/PgoskcHrsQocd17b5r8ZzCcrrf5fJylx7dQmmbj22tDwUNJJm9RrpD7K2SPjgxftruzKB2ytGvdREH8+CiyRweG07Xr3v+E2fUAAAAQiTF5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTB4Anthj0er1er9efrJ7kBwEAmjwAAACEoskDAABAJJo8AAAARKLJAwAAQCSaPAAAAESiyQPAJ3S61PxqMej3e6V+fzBZtK9Av1pMakf3B1cObT6l+QeUv1GvN1hcnD/pt78IAJ+PJg8An9rPSb83mm2KovpKUWyWs1FjZ15N+r3RbFk7uti0HNp+SvkD+ienTdfzbP+vzez0+60m4+X+5HScr6ev+Y8DgOekyQPAJ1YsZ8ui+aXzQp2sJv1R88GbWf/7v00vtJ+SJEmxmZ3sPt/c5es9fvkybPleAPCpaPIA8Nml2Xie7/by+Tgtv775u1blj436/PgsTZKiaOjrLafs8nl2+BnFcny9y+vxANBAkweAzy2bb9cv07IkD6cv27ws8//+U9Xs1Y+8aDl+fTzhxOJrWcJPT0mG0/U2P3T2Yvn1ZI79X+W32nyfrPR4AGikyQPAZ5aO/7p48nz452hfp4v1z8OXqiLfdHwyfPmWXXxx9c9hwn32reHh9mHV2U9G/pPhy/Lw9SIfj/R4AGiiyQPAJ5aO/ryrIv9cF1ePn/5xUeXLU7I/mhepG/7+2/4ftZH/JKl1+XLCvh4PAGc0eQDgbr/93tKpvwzOJthXQ/KbWa/ZbNPyQ47j8okeDwANNHkA4H/m+FB+khT5j9sb1gPA56LJAwB3O5sJf1TOpb+UzXfXbc/G3GtL3ifJxfr2AIAmDwDcVk6ebxshr+bSV9oeg7+pWvI+m1fr2+vyAFCnyQMANx2Xs29q1Wej6HvlInhtPXw16e+flx/U165fDA6Pz2fz9bRa316XB4A6TR4AuO240VyxHPUHi7JXr1aLQX902eOT2t7wxXLUH0wWxypeP+lkW7uqxx++WtuTTpcHgIomDwDcY7qelzvNFZvZ6LAA/Wg02xRJkmWXG8rX16AvNsvqlOqkJEmS7NvxKflaj6/Wq693+a/1wXsA+MQ0eQDgPtN1Ps/Shhey+fqPxjOGL9vmM5IkSZI0m+frakC+qcfvv0c5G2AzG+jyAJBo8gDA/YbT9Tafj7P0uN17Ns53xzp+abre7k5PSZI0TbN5nm/X08vx+JNR+vJbzHV5AKjp7Xa7j/4dAAAAgHsZkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASDR5AAAAiESTBwAAgEg0eQAAAIhEkwcAAIBINHkAAACIRJMHAACASP4DD1IVxtDAuXkAAAAASUVORK5CYII=" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuQ0VfdGFibGVSaG9VbmlmXG5gYGBcbmBgYCJ9 -->
```r
```r
CE_tableRhoUnif
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiICAgICAgIGVzdGltYXRlcyAgICAgICAgc2QgcXVhbnRpbGUwMjUgcXVhbnRpbGU5NzUgQ0lsZW5ndGg5NVxuTklFICAwLjAwMzI0NDQ5NCAwLjEzMzM0NDkgIC0wLjI2NjM4MzUgICAwLjIxNjIzNjkgIDAuNDgyNjIwNFxuTkRFIC0zLjI0MTI2NzkwOSAwLjY5NjU5NTYgIC00LjQ3OTg3OTYgIC0yLjEwMzIzNzQgIDIuMzc2NjQyMlxuQVRFIC0zLjIzODAyMzQxNSAwLjc0NzE4MzYgIC00LjY1MDg2NTUgIC0yLjEyMzg3MzYgIDIuNTI2OTkxOVxuIn0= -->
estimates sd quantile025 quantile975 CIlength95NIE 0.003244494 0.1333449 -0.2663835 0.2162369 0.4826204 NDE -3.241267909 0.6965956 -4.4798796 -2.1032374 2.3766422 ATE -3.238023415 0.7471836 -4.6508655 -2.1238736 2.5269919
<!-- rnb-output-end -->
<!-- rnb-chunk-end -->
<!-- rnb-text-begin -->
\newpage
### dist. of f(M)
<!-- rnb-text-end -->
<!-- rnb-chunk-begin -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuc2V0LnNlZWQoMSlcbk0gPSBMSVRFZGF0YSRhdHRcblxuZXBzID0gMC4xXG5NID0gKE0qKGRpZmYocmFuZ2UoTSkpLTIqZXBzKSkrZXBzXG5cbk1DTUNyZXN1bHQgPSBFRFBtZWRpYXRpb25NQ01DKFksIE0sIFYsIFosIEMsXG4gICAgICAgICAgICAgICAgICAgICAgICAgICAgICBnaWJic19pdGVyLCBnaWJic19idXJuaW4sIGdpYmJzX3RoaW4sXG4gICAgICAgICAgICAgICAgICAgICAgICAgICAgICBELCBudW1fTUMsIG51bV9NQ19wcmlvcilcbmBgYFxuYGBgIn0= -->
```r
```r
set.seed(1)
M = LITEdata$att
eps = 0.1
M = (M*(diff(range(M))-2*eps))+eps
MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
gibbs_iter, gibbs_burnin, gibbs_thin,
D, num_MC, num_MC_prior)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Bur-In End 5000 Time: Tue Feb 21 18:47:03 2023 Gibbs Iteration 250 ( 5 %) Time: Tue Feb 21 18:47:11 2023 Gibbs Iteration 500 ( 10 %) Time: Tue Feb 21 18:47:18 2023 Gibbs Iteration 750 ( 15 %) Time: Tue Feb 21 18:47:26 2023 Gibbs Iteration 1000 ( 20 %) Time: Tue Feb 21 18:47:34 2023 Gibbs Iteration 1250 ( 25 %) Time: Tue Feb 21 18:47:41 2023 Gibbs Iteration 1500 ( 30 %) Time: Tue Feb 21 18:47:49 2023 Gibbs Iteration 1750 ( 35 %) Time: Tue Feb 21 18:47:56 2023 Gibbs Iteration 2000 ( 40 %) Time: Tue Feb 21 18:48:03 2023 Gibbs Iteration 2250 ( 45 %) Time: Tue Feb 21 18:48:11 2023 Gibbs Iteration 2500 ( 50 %) Time: Tue Feb 21 18:48:19 2023 Gibbs Iteration 2750 ( 55 %) Time: Tue Feb 21 18:48:26 2023 Gibbs Iteration 3000 ( 60 %) Time: Tue Feb 21 18:48:34 2023 Gibbs Iteration 3250 ( 65 %) Time: Tue Feb 21 18:48:41 2023 Gibbs Iteration 3500 ( 70 %) Time: Tue Feb 21 18:48:49 2023 Gibbs Iteration 3750 ( 75 %) Time: Tue Feb 21 18:48:56 2023 Gibbs Iteration 4000 ( 80 %) Time: Tue Feb 21 18:49:04 2023 Gibbs Iteration 4250 ( 85 %) Time: Tue Feb 21 18:49:11 2023 Gibbs Iteration 4500 ( 90 %) Time: Tue Feb 21 18:49:19 2023 Gibbs Iteration 4750 ( 95 %) Time: Tue Feb 21 18:49:26 2023 Gibbs Iteration 5000 ( 100 %) Time: Tue Feb 21 18:49:34 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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-->
```r
```r
{
# Significance Level alpha
level = 0.05
quantile_alpha = c(level/2,1-level/2)
# the number of Gibbs Sampler stored
n_MCMC = MCMCresult$constants$n_MCMC
# Define interation check
iter_check = floor(n_MCMC/10)
M0_mc = list(NA)
Mr_mc = list(NA)
M1_mc = list(NA)
N = MCMCresult$constants$N
D = MCMCresult$constants$D
num_MC = MCMCresult$constants$num_MC
p_V = MCMCresult$constants$p_V
p_Z = MCMCresult$constants$p_Z
p_C1 = MCMCresult$constants$p_C1
p_C2 = MCMCresult$constants$p_C2
f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
a_Ysig2 = MCMCresult$priors$a_Ysig2
b_Ysig2 = MCMCresult$priors$b_Ysig2
a_Ybeta = MCMCresult$priors$a_Ybeta
B_Ybeta = MCMCresult$priors$B_Ybeta
a_Msig2 = MCMCresult$priors$a_Msig2
b_Msig2 = MCMCresult$priors$b_Msig2
a_Mbeta = MCMCresult$priors$a_Mbeta
B_Mbeta = MCMCresult$priors$B_Mbeta
a_Vsig2 = MCMCresult$priors$a_Vsig2
b_Vsig2 = MCMCresult$priors$b_Vsig2
a_Vbeta = MCMCresult$priors$a_Vbeta
B_Vbeta = MCMCresult$priors$B_Vbeta
a_pi = MCMCresult$priors$a_pi
b_pi = MCMCresult$priors$b_pi
a_mu = MCMCresult$priors$a_mu
b_mu = MCMCresult$priors$b_mu
a_tau2 = MCMCresult$priors$a_tau2
b_tau2 = MCMCresult$priors$b_tau2
alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
rho = runif(n_MCMC)
# End initial values ------------------------------------------------------------
for (post_reps in 1:n_MCMC) {
Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
rho_mc = rho[post_reps] * rep(1,D)
YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
ZpiPars_array = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
XpiPars_array = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
XmuPars_array = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
alpha_theta = alpha_theta_draws[post_reps]
alpha_omega = alpha_omega_draws[post_reps]
MCresult = EDPpostmc_concon(p_C1, p_C2,
n_k, n_rk, Ky, Kyx, max_Kx_Sy,
D, num_MC, rho_mc,
YbetaPars, Ysig2Pars,
MbetaPars, Msig2Pars,
VbetaPars_array, Vsig2Pars_array,
ZpiPars_array, XpiPars_array,
XmuPars_array, Xtau2Pars_array,
alpha_theta, alpha_omega,
f0_z0_mc, f0_z1_mc,
YbetaPrior_mc,
MbetaPrior_mc, Msig2Prior_mc,
VbetaPrior_mc, Vsig2Prior_mc,
a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
M0_mc[[post_reps]] = MCresult$M0_mc
Mr_mc[[post_reps]] = MCresult$Mr_mc
M1_mc[[post_reps]] = MCresult$M1_mc
if (post_reps %% iter_check == 0){
cat(\Post-Processing\,post_reps,\(\,(post_reps/n_MCMC)*100,\%)\,\Time:\,date(),\\n\)
}
}
distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:49:35 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:49:35 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:49:36 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:49:36 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:49:37 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:49:37 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:49:38 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:49:38 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:49:38 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:49:39 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTTBfbWMgPSB1bmxpc3QoZGlzdE0kTTBfbWMpXG5Ncl9tYyA9IHVubGlzdChkaXN0TSRNcl9tYylcbk0xX21jID0gdW5saXN0KGRpc3RNJE0xX21jKVxuXG5tZWFuKE0pXG5gYGBcbmBgYCJ9 -->
```r
```r
M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)
mean(M)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuNTI0NzQ0XG4ifQ== -->
[1] 0.524744
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTBdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==0])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuNTE5MjQyOVxuIn0= -->
[1] 0.5192429
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTFdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==1])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuNTMwNjU1NFxuIn0= -->
[1] 0.5306554
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)
# print(\dist. of M based on the data\)
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Data\,col=\green\)
legend(\topright\, legend=c(\M\, \M[Z==0]\, \M[Z==1]\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# print(\dist. of M based on the G-computation\)
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\G-computation\,col=\green\)
abline(v = 0, col = \black\, lwd = 2)abline(v = 1, col = \black\, lwd = 2)
legend(\topright\, legend=c(\M0\, \Mr\, \M1\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDEwMClcbmhpc3QoTSx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE06IGRhdGFcXClcbmBgYFxuYGBgIn0= -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTBdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0wXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==0]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTFdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0xXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==1]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDM1MClcbmhpc3QoTTBfbWNbd2hpY2goKE0wX21jPnhsaW1fQ0VbMV0pKihNMF9tYzx4bGltX0NFWzJdKT09MSldLDFlMyx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE0wOiBHLWNvbXB1dGF0aW9uXFwpXG5gYGBcbmBgYCJ9 -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M0: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNcl9tY1t3aGljaCgoTXJfbWM+eGxpbV9DRVsxXSkqKE1yX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTXI6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Mr: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNMV9tY1t3aGljaCgoTTFfbWM+eGxpbV9DRVsxXSkqKE0xX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTTE6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M1: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIC0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS1cbiMgLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLVxuIyAtLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tXG5yaG8gPSBcXHVuaWZcXFxuUE9TVHJlc3VsdFJob1VuaWYgPSBFRFBtZWRpYXRpb25QT1NUKE1DTUNyZXN1bHQsIGVzdHR5cGUsIHJobywgc2F2ZV9jbHVzdGVyKVxuYGBgXG5gYGAifQ== -->
```r
```r
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = \unif\
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiUG9zdC1Qcm9jZXNzaW5nIDUgKCAxMCAlKSBUaW1lOiBUdWUgRmViIDIxIDE4OjQ5OjQ0IDIwMjMgXG5Qb3N0LVByb2Nlc3NpbmcgMTAgKCAyMCAlKSBUaW1lOiBUdWUgRmViIDIxIDE4OjQ5OjQ0IDIwMjMgXG5Qb3N0LVByb2Nlc3NpbmcgMTUgKCAzMCAlKSBUaW1lOiBUdWUgRmViIDIxIDE4OjQ5OjQ1IDIwMjMgXG5Qb3N0LVByb2Nlc3NpbmcgMjAgKCA0MCAlKSBUaW1lOiBUdWUgRmViIDIxIDE4OjQ5OjQ1IDIwMjMgXG5Qb3N0LVByb2Nlc3NpbmcgMjUgKCA1MCAlKSBUaW1lOiBUdWUgRmViIDIxIDE4OjQ5OjQ2IDIwMjMgXG5Qb3N0LVByb2Nlc3NpbmcgMzAgKCA2MCAlKSBUaW1lOiBUdWUgRmViIDIxIDE4OjQ5OjQ2IDIwMjMgXG5Qb3N0LVByb2Nlc3NpbmcgMzUgKCA3MCAlKSBUaW1lOiBUdWUgRmViIDIxIDE4OjQ5OjQ2IDIwMjMgXG5Qb3N0LVByb2Nlc3NpbmcgNDAgKCA4MCAlKSBUaW1lOiBUdWUgRmViIDIxIDE4OjQ5OjQ3IDIwMjMgXG5Qb3N0LVByb2Nlc3NpbmcgNDUgKCA5MCAlKSBUaW1lOiBUdWUgRmViIDIxIDE4OjQ5OjQ3IDIwMjMgXG5Qb3N0LVByb2Nlc3NpbmcgNTAgKCAxMDAgJSkgVGltZTogVHVlIEZlYiAyMSAxODo0OTo0OCAyMDIzIFxuIn0= -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:49:44 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:49:44 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:49:45 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:49:45 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:49:46 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:49:46 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:49:46 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:49:47 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:49:47 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:49:48 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTklFX3RhYmxlUmhvVW5pZiA9IFBPU1RyZXN1bHRSaG9VbmlmJE5JRV9yZXN1bHRfbWNcbk5ERV90YWJsZVJob1VuaWYgPSBQT1NUcmVzdWx0UmhvVW5pZiROREVfcmVzdWx0X21jXG5BVEVfdGFibGVSaG9VbmlmID0gUE9TVHJlc3VsdFJob1VuaWYkQVRFX3Jlc3VsdF9tY1xuXG5DRV90YWJsZVJob1VuaWYgPSByYmluZChOSUVfdGFibGVSaG9VbmlmLE5ERV90YWJsZVJob1VuaWYsQVRFX3RhYmxlUmhvVW5pZilcbnJvd25hbWVzKENFX3RhYmxlUmhvVW5pZikgPSBjKFxcTklFXFwsXFxOREVcXCxcXEFURVxcKVxuXG5OSUVyaG9VbmlmID0gUE9TVHJlc3VsdFJob1VuaWYkTklFXG5OREVyaG9VbmlmID0gUE9TVHJlc3VsdFJob1VuaWYkTkRFXG5BVEVyaG9VbmlmID0gUE9TVHJlc3VsdFJob1VuaWYkQVRFXG5cbnE5NSA9IHF1YW50aWxlKGMoTklFcmhvVW5pZixOREVyaG9VbmlmLEFURXJob1VuaWYpLGMoMC4wMjUsIDAuOTc1KSlcbnlsaW1fQ0U9YyhmbG9vcihtaW4ocTk1KSksY2VpbGluZyhtYXgoYyhxOTUpKSkpXG5wbG90KHNvcnQoTklFcmhvVW5pZiksY29sPVxccmVkXFwseWxpbT15bGltX0NFKTtwYXIobmV3PVQpXG5wbG90KHNvcnQoTkRFcmhvVW5pZiksY29sPVxcYmx1ZVxcLHlsaW09eWxpbV9DRSk7cGFyKG5ldz1UKVxuYGBgXG5gYGByXG5wbG90KHNvcnQoQVRFcmhvVW5pZiksY29sPVxcZ3JlZW5cXCx5bGltPXlsaW1fQ0UpXG5gYGBcbmBgYCJ9 -->
```r
```r
NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc
CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c(\NIE\,\NDE\,\ATE\)
NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE
q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col=\red\,ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col=\blue\,ylim=ylim_CE);par(new=T)plot(sort(ATErhoUnif),col=\green\,ylim=ylim_CE)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuQ0VfdGFibGVSaG9VbmlmXG5gYGBcbmBgYCJ9 -->
```r
```r
CE_tableRhoUnif
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiICAgICAgZXN0aW1hdGVzICAgICAgICBzZCBxdWFudGlsZTAyNSBxdWFudGlsZTk3NSBDSWxlbmd0aDk1XG5OSUUgLTAuMDI3OTA4NDQgMC4xMzAyNjEyICAtMC4yMDYxMTE2ICAgMC4zMTAzMDY1ICAwLjUxNjQxODFcbk5ERSAtMy4xMDMyMjMyMCAwLjY3MzQ4NzIgIC00LjM1NTgxMTkgIC0xLjc4ODYxNjkgIDIuNTY3MTk1MVxuQVRFIC0zLjEzMTEzMTYzIDAuNjU0ODkyNCAgLTQuMjQ2NzU2OSAgLTEuNzk5MzIxMyAgMi40NDc0MzU2XG4ifQ== -->
estimates sd quantile025 quantile975 CIlength95NIE -0.02790844 0.1302612 -0.2061116 0.3103065 0.5164181 NDE -3.10322320 0.6734872 -4.3558119 -1.7886169 2.5671951 ATE -3.13113163 0.6548924 -4.2467569 -1.7993213 2.4474356
<!-- rnb-output-end -->
<!-- rnb-chunk-end -->
<!-- rnb-text-begin -->
\newpage
### dist. of f(M)
<!-- rnb-text-end -->
<!-- rnb-chunk-begin -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuc2V0LnNlZWQoMSlcbk0gPSBMSVRFZGF0YSRhdHRcblxuZXBzID0gMC4xXG5NID0gKE0qKGRpZmYocmFuZ2UoTSkpLTIqZXBzKSkrZXBzXG5NID0gbG9nKE0vKDEtTSkpXG5cbk1DTUNyZXN1bHQgPSBFRFBtZWRpYXRpb25NQ01DKFksIE0sIFYsIFosIEMsXG4gICAgICAgICAgICAgICAgICAgICAgICAgICAgICBnaWJic19pdGVyLCBnaWJic19idXJuaW4sIGdpYmJzX3RoaW4sXG4gICAgICAgICAgICAgICAgICAgICAgICAgICAgICBELCBudW1fTUMsIG51bV9NQ19wcmlvcilcbmBgYFxuYGBgIn0= -->
```r
```r
set.seed(1)
M = LITEdata$att
eps = 0.1
M = (M*(diff(range(M))-2*eps))+eps
M = log(M/(1-M))
MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
gibbs_iter, gibbs_burnin, gibbs_thin,
D, num_MC, num_MC_prior)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Bur-In End 5000 Time: Tue Feb 21 18:52:49 2023 Gibbs Iteration 250 ( 5 %) Time: Tue Feb 21 18:52:56 2023 Gibbs Iteration 500 ( 10 %) Time: Tue Feb 21 18:53:04 2023 Gibbs Iteration 750 ( 15 %) Time: Tue Feb 21 18:53:11 2023 Gibbs Iteration 1000 ( 20 %) Time: Tue Feb 21 18:53:19 2023 Gibbs Iteration 1250 ( 25 %) Time: Tue Feb 21 18:53:27 2023 Gibbs Iteration 1500 ( 30 %) Time: Tue Feb 21 18:53:35 2023 Gibbs Iteration 1750 ( 35 %) Time: Tue Feb 21 18:53:43 2023 Gibbs Iteration 2000 ( 40 %) Time: Tue Feb 21 18:53:51 2023 Gibbs Iteration 2250 ( 45 %) Time: Tue Feb 21 18:53:58 2023 Gibbs Iteration 2500 ( 50 %) Time: Tue Feb 21 18:54:06 2023 Gibbs Iteration 2750 ( 55 %) Time: Tue Feb 21 18:54:14 2023 Gibbs Iteration 3000 ( 60 %) Time: Tue Feb 21 18:54:21 2023 Gibbs Iteration 3250 ( 65 %) Time: Tue Feb 21 18:54:29 2023 Gibbs Iteration 3500 ( 70 %) Time: Tue Feb 21 18:54:36 2023 Gibbs Iteration 3750 ( 75 %) Time: Tue Feb 21 18:54:44 2023 Gibbs Iteration 4000 ( 80 %) Time: Tue Feb 21 18:54:51 2023 Gibbs Iteration 4250 ( 85 %) Time: Tue Feb 21 18:54:59 2023 Gibbs Iteration 4500 ( 90 %) Time: Tue Feb 21 18:55:06 2023 Gibbs Iteration 4750 ( 95 %) Time: Tue Feb 21 18:55:14 2023 Gibbs Iteration 5000 ( 100 %) Time: Tue Feb 21 18:55:21 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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-->
```r
```r
{
# Significance Level alpha
level = 0.05
quantile_alpha = c(level/2,1-level/2)
# the number of Gibbs Sampler stored
n_MCMC = MCMCresult$constants$n_MCMC
# Define interation check
iter_check = floor(n_MCMC/10)
M0_mc = list(NA)
Mr_mc = list(NA)
M1_mc = list(NA)
N = MCMCresult$constants$N
D = MCMCresult$constants$D
num_MC = MCMCresult$constants$num_MC
p_V = MCMCresult$constants$p_V
p_Z = MCMCresult$constants$p_Z
p_C1 = MCMCresult$constants$p_C1
p_C2 = MCMCresult$constants$p_C2
f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
a_Ysig2 = MCMCresult$priors$a_Ysig2
b_Ysig2 = MCMCresult$priors$b_Ysig2
a_Ybeta = MCMCresult$priors$a_Ybeta
B_Ybeta = MCMCresult$priors$B_Ybeta
a_Msig2 = MCMCresult$priors$a_Msig2
b_Msig2 = MCMCresult$priors$b_Msig2
a_Mbeta = MCMCresult$priors$a_Mbeta
B_Mbeta = MCMCresult$priors$B_Mbeta
a_Vsig2 = MCMCresult$priors$a_Vsig2
b_Vsig2 = MCMCresult$priors$b_Vsig2
a_Vbeta = MCMCresult$priors$a_Vbeta
B_Vbeta = MCMCresult$priors$B_Vbeta
a_pi = MCMCresult$priors$a_pi
b_pi = MCMCresult$priors$b_pi
a_mu = MCMCresult$priors$a_mu
b_mu = MCMCresult$priors$b_mu
a_tau2 = MCMCresult$priors$a_tau2
b_tau2 = MCMCresult$priors$b_tau2
alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
rho = runif(n_MCMC)
# End initial values ------------------------------------------------------------
for (post_reps in 1:n_MCMC) {
Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
rho_mc = rho[post_reps] * rep(1,D)
YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
ZpiPars_array = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
XpiPars_array = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
XmuPars_array = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
alpha_theta = alpha_theta_draws[post_reps]
alpha_omega = alpha_omega_draws[post_reps]
MCresult = EDPpostmc_concon(p_C1, p_C2,
n_k, n_rk, Ky, Kyx, max_Kx_Sy,
D, num_MC, rho_mc,
YbetaPars, Ysig2Pars,
MbetaPars, Msig2Pars,
VbetaPars_array, Vsig2Pars_array,
ZpiPars_array, XpiPars_array,
XmuPars_array, Xtau2Pars_array,
alpha_theta, alpha_omega,
f0_z0_mc, f0_z1_mc,
YbetaPrior_mc,
MbetaPrior_mc, Msig2Prior_mc,
VbetaPrior_mc, Vsig2Prior_mc,
a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
M0_mc[[post_reps]] = MCresult$M0_mc
Mr_mc[[post_reps]] = MCresult$Mr_mc
M1_mc[[post_reps]] = MCresult$M1_mc
if (post_reps %% iter_check == 0){
cat(\Post-Processing\,post_reps,\(\,(post_reps/n_MCMC)*100,\%)\,\Time:\,date(),\\n\)
}
}
distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:55:22 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:55:23 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:55:23 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:55:24 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:55:24 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:55:25 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:55:25 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:55:26 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:55:26 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:55:26 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTTBfbWMgPSB1bmxpc3QoZGlzdE0kTTBfbWMpXG5Ncl9tYyA9IHVubGlzdChkaXN0TSRNcl9tYylcbk0xX21jID0gdW5saXN0KGRpc3RNJE0xX21jKVxuXG5tZWFuKE0pXG5gYGBcbmBgYCJ9 -->
```r
```r
M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)
mean(M)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuMTAwMjQ0NFxuIn0= -->
[1] 0.1002444
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTBdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==0])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuMDg4MDU5MjlcbiJ9 -->
[1] 0.08805929
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTFdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==1])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuMTEzMzM4MVxuIn0= -->
[1] 0.1133381
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)
# print(\dist. of M based on the data\)
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Data\,col=\green\)
legend(\topright\, legend=c(\M\, \M[Z==0]\, \M[Z==1]\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# print(\dist. of M based on the G-computation\)
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\G-computation\,col=\green\)
abline(v = 0, col = \black\, lwd = 2)abline(v = 1, col = \black\, lwd = 2)
legend(\topright\, legend=c(\M0\, \Mr\, \M1\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDEwMClcbmhpc3QoTSx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE06IGRhdGFcXClcbmBgYFxuYGBgIn0= -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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1dseuXvRvZWWMPvEztUG5vt+0OXBfps8dH831+8+GH3Sk9D7dDR8fvEDtXGZrkSr++1n006+zmlq/ywJ/h02KER+H1ih2pj81yJox9u31698PJ3PS/CDD4ddmgEfp/YodrY3Ffi6NfHe0+u+CrM4NNhh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3iR2qjRGvBDFTY4dG4PeJHaqNEa8EMVNjh0bg94kdqo0RrwQxU2OHRuD3ScUOneJFR2QirknM1NihERL0SXTCDB0anbDK2SauSczUeM4ilOyT8IEJdo6OyERck5ip8ZxFKNkn4QMT7BwdkYm4JjFT4zmLULJPwgcm2Dk6IhNxTWKmxnMWoWSfhA9MsHN0RCbimsRMjecsQsk+CR+YYOfoiEzENYmZGs9ZhJJ9Ej4wwc7REZmIaxIzNZ6zCCX7JHxggp2jIzIR1yRmajxnEUr2SfjABDtHR2QirknM1HjOIpTsk/CBCXaOjshEXJOYqfGcRSjZJ+EDE+wcHZGJuCYxU+M5i1CyT8IHJtg5OiITcU1ipsZzFqFkn4QPTLBzdEQm4prETI3nLELJPgkfmGDn6IhMxDWJmRrPWYSSfRI+MMHO0RGZiGsSMzWeswgl+yR8YIKdoyMyEdckZmo8ZxFK9kn4wAQ7R0dkIq5JzNR4ziKU7JPwgQl2jo7IRFyTmKnxnEUo2SfhAxPsHB2RibgmMVPjOYtQsk/CBybYOToiE3FNYqbGcxahZJ+ED0ywc3REJuKaxEyN5yxCyT4JH5hg5+iITMQ1iZkaz1mEkn0SPjDBztERmYhrEjM1nrMIJfskfGCCnaMjMhHXJGZqPGcRSvZJ+MAEO0dHZJptzTfP9u7fXriz9+SPK/5R8EPvOYtQsk/CBybYOToi00xrPv90WrPzDSFTBM9ZhJJ9Ej4wwc7REZlmWfPo4XTBzZfbzhTDcxahZJ+ED0ywc3REpjnWXFXonaftQ/g3v96/YomCH3rPWYSSfRI+MMHO0RGZ5ljzYPHR+4P1NzzfnaYvN//z4IfecxahZJ+ED0ywc3REphnWXD4NvdCYB1d6Igp+6D1nEUr2SfjABDtHR2SaYc0/7007355/06vd6cYvGw8AP/Seswgl+yR8YIKdoyMyzdOhFwvzkjf9BfBD7zmLULJPwgcm2Dk6IpPPQ6/EcxahZJ+ED0ywc3REpjnW3H/n86GLt9za/M+DH3rPWYSSfRI+MMHO0RGZ5ljzcJqmL9a+hHT0/eIND97//heBH3rPWYSSfRI+MMHO0RGZZllzf/lt9Z89+enFwu/PHu1OV3oaaoeOrmSfhA9MsHN0RKZ51jy4+HNKd7efKYTnLELJPgkfmGDn6IhMM635+tF6g37+MyFTBM9ZhJJ9Ej4wwc7REZnmW/PNb88e7+19/eTHq75skx06upJ9Ej4wwc7REZmIaxIzNZ6zCCX7JHxggp2jIzJtf82Lnzpd2Hak9/OcRSjZJ+EDE+wcHZFprjWP/nP1zU1HP9y/ffvzp1f7s+CH3nMWoWSfhA9MsHN0RKZ51nz91fHPJf1z9/iJ5SfffvCPzJ4phOcsQsk+CR+YYOfoiEyzrHm4qM5lh659i9MVvsXeDh1dyT4JH5hg5+iITHOs+WpRoX/7x8vV/978efWs9Co/Lm+Hjq5kn4QPTLBzdESmmX5efvVqoSf/e9kril53piCeswgl+yR8YIKdoyMyzfQazA/W/vft6ifofQ3mrOfskm+c+Fj4B9EORUZkmvH1Q9deNNTXD018zuyTkIjhAxPsHB2RyQ69kornzD4JiRg+MMHO0RGZ5vlY/vg1mPdPX4v51a4fy6c9Z/ZJSMTwgQl2jo7INMeaJ7+B7vD0K0kHvgZz3nNmn4REDB+YYOfoiExzfW/TreMvzB8/EX1+tW8QBT/0Fc+ZfRISMXxggp2jIzLNsubye+t3/uWn1Uf1n/+vZ/cnX4M58TmzT0Iihg9MsHN0RKZ51jz5Gc9Ttzb/bKgdCmOfhEQMH5hg5+iITNfyGsw73xAyRah4zuyTkIjhAxPsHB2Rab41f/9h7/bS3r9d7VXs7VAY+yQkYvjABDtHR2QirknM1FQ8Z/ZJSMTwgQl2jo7IRFyTmKmpeM7sk5CI4QMT7BwdkYm4JjFTU/Gc2SchEcMHJtg5OiITcU1ipqbiObNPQiKGD0ywc3REJuKaxExNxXNmn4REDB+YYOfoiEzENYmZmornzD4JiRg+MMHO0RGZiGsSMzUVz5l9EhIxfGCCnaMjMhHXJGZqKp4z+yQkYvjABDtHR2QirknM1FQ8Z/ZJSMTwgQl2jo7IRFyTmKmpeM7sk5CI4QMT7BwdkYm4JjFTU/Gc2SchEcMHJtg5OiITcU1ipqbiObNPQiKGD0ywc3REJuKaxExNxXNmn4REDB+YYOfoiEzENYmZmornzD4JiRg+MMHO0RGZiGsSMzUVz5l9EhIxfGCCnaMjMhHXJGZqKp4z+yQkYvjABDtHR2QirknM1FQ8Z/ZJSMTwgQl2jo7IRFyTmKmpeM7sk5CI4QMT7BwdkYm4JjFTU/Gc2SchEcMHJtg5OiITcU1ipqbiObNPQiKGD0ywc3REJuKaxExNxXNmn4REDB+YYOfoiEzENYmZmornzD4JiRg+MMHO0RGZiGsSMzUVz5l9EhIxfGCCnaMjMhHXJGZqKp4z+yQkYvjABDtHR2QirknM1FQ8Z/ZJSMTwgQl2jo7IRFyTmKmpeM7sk5CI4QMT7BwdkYm4JjFTU/Gc2SchEcMHJtg5OiITcU1ipqbiObNPQiKGD0ywc3REJuKaxExNxXNmn4REDB+YYOfoiEzENYmZmornzD4JiRg+MMHO0RGZiGsSMzUVz5l9EhIxfGCCnaMjMhHXJGZqKp4z+yQkYvjABDtHR2QirknM1FQ8Z/ZJSMTwgQl2jo7IRFyTmKmpeM7sk5CI4QMT7BwdkYm4JjFTU/Gc2SchEcMHJtg5OiITcU1ipqbiObNPQiKGD0ywc3REJuKaxExNxXNmn4REDB+YYOfoiEzENYmZmornzD4JiRg+MMHO0RGZiGsSMzUVz5l9EhIxfGCCnaMjMhHXJGZqKp4z+yQkYvjABDtHR2QirknM1FQ8Z/ZJSMTwgQl2jo7IRFyTmKmpeM7sk5CI4QMT7BwdkYm4JjFTU/Gc2SchEcMHJtg5OiITcU1ipqbiObNPQiKGD0ywc3REJuKaxExNxXNmn4REDB+YYOfoiEzENYmZmornzD4JiRg+MMHO0RGZiGsSMzUVz5l9EhIxfGCCnaMjMhHXJGZqKp4z+yQkYvjABDtHR2QirknM1FQ8Z/ZJSMTwgQl2jo7IRFyTmKmpeM7sk5CI4QMT7BwdkYm4JjFTU/Gc2SchEcMHJtg5OiITcU1ipqbiObNPQiKGD0ywc3REJuKaxExNxXNmn4REDB+YYOfoiEzENYmZmornzD4JiRg+MMHO0RGZiGsSMzUVz5l9EhIxfGCCnaMjMhHXJGZqKp4z+yQkYvjABDtHR2QirknM1FQ8Z/ZJSMTwgQl2jo7IRFyTmKmpeM7sk5CI4QMT7BwdkYm4JjFTU/Gc2SchEcMHJtg5OiITcU1ipqbiObNPQiKGD0ywc3REJuKaxExNxXNmn4REDB+YYOfoiEzENYmZmornzD4JiRg+MMHO0RGZiGsSMzUVz5l9EhIxfGCCnaMjMhHXJGZqKp4z+yQkYvjABDtHR2QirknM1FQ8Z/ZJSMTwgQl2jo7IRFyTmKmpeM7sk5CI4QMT7BwdkYm4JjFTU/Gc2SchEcMHJtg5OiITcU1ipqbiObNPQiKGD0ywc3REJuKaxExNxXNmn4REDB+YYOfoiEzENYmZmornzD4JiRg+MMHO0RGZiGsSMzUVz5l9EhIxfGCCnaMjMhHXJGZqKp4z+yQkYvjABDtHR2QirknM1FQ8Z/ZJSMTwgQl2jo7IRFyTmKmpeM7sk5CI4QMT7BwdkYm4JjFTU/Gc2SchEcMHJtg5OiLTbGu+ebZ3//bCnb0nf1zxj4If+ornzD4JiRg+MMHO0RGZZlrz+afTmp1vCJkiVDxn9klIxPCBCXaOjsg0y5pHD6cLbr7cdqYYFc+ZfRISMXxggp2jIzLNseaqQu88bR/Cv/n1/hVLFPzQVzxn9klIxPCBCXaOjsg0x5oHi4/eH6y/4fnuNH25+Z8HP/QVz5l9EhIxfGCCnaMjMs2w5vJp6IXGPLjSE1HwQ1/xnGXok3DRCe3Qcc2w5p/3pp1vz7/p1e5045eNB4Af+ornLEOf4AfaoeOap0MvFuYlb/oL4Ie+4jnL0Cf4gXbouHweeiUVz1mGPsEPtEPHNcea++98PnTxllub/3nwQ1/xnGXoE/xAO3Rcc6x5OE3TF2tfQjr6fvGGB+9//4vAD33Fc5ahT/AD7dBxzbLm/vIrm589+enFwu/PHu1OV3oaaoeyZOgT/EA7dFzzrHlw8VtF7m4/U4iK5yxDn+AH2qHjmmnN14/WG/TznwmZIlQ8Zxn6BD/QDh3XfGu++e3Z4729r5/8eNWXbbJDWTL0CX6gHTou4prETE3Fc5ahT/AD7dBxbX/NS37QbtuR3q/iOcvQJ/iBdui4Zl/zz/u372z+7fUr4Ie+4jnL0Cf4gXbouObv0Cv9mOcK+KGveM4y9Al+oB06Ljv0Siqeswx9gh9oh45rjp+XX/0epRPLXwryt+XvVfLn5ZOeswx9gh9oh45rntccuYSvOZL1nGXoE/xAO3RcM70Gsx06zjnL0Cf4gXbouGZZ85+7087T9s9+PjT7OcvQJ/iBdui45lnz9VfTdPf4lZvs0OznLEOf4AfaoeOaac2j76bpk9VPyduh2c9Zhj7BD7RDxzXbms8XH89/89YOvfZzdsVfvraB+J3rDbRDxzXfmq8fTtPnL+3Q6z5nJfsEP9AOHdeMay5fvn7nqR16zeesZJ/gB9qh45p1zVe70/SZHXq956xkn+AH2qHjmnfNo0dX/NbQFfBDn+CclewT/EA7dFxzr/l81w693nNWsk/wA+3Qcc2+5uvHe1+//PC7rQM/9AnOWck+wQ+0Q8dFXJOYqUlwzkr2CX6gHTou4prETE2Cc1ayT/AD7dBxEdckZmoSnLOSfYIfaIeOi7gmMVOT4JyV7BP8QDt0XMQ1iZmaBOesZJ/gB9qh4yKuSczUJDhnJfsEP9AOHRdxTWKmJsE5K9kn+IF26LiIaxIzNQnOWck+wQ+0Q8dFXJOYqUlwzkr2CX6gHTou4prETE2Cc1ayT/AD7dBxEdckZmoSnLOSfYIfaIeOi7gmMVOT4JyV7BP8QDt0XMQ1iZmaBOesZJ/gB9qh4yKuSczUJDhnJfsEP9AOHRdxTWKmJsE5K9kn+IF26LiIaxIzNQnOWck+wQ+0Q8dFXJOYqUlwzkr2CX6gHTou4prETE2Cc1ayT/AD7dBxEdckZmoSnLOSfYIfaIeOi7gmMVOT4JyV7BP8QDt0XMQ1iZmaBOesZJ/gB9qh4yKuSczUJDhnJfsEP2l57XcAABQ9SURBVNAOHRdxTWKmJsE5K9kn+IF26LiIaxIzNQnOWck+wQ+0Q8dFXJOYqUlwzkr2CX6gHTou4prETE2Cc1ayT/AD7dBxEdckZmoSnLOSfYIfaIeOi7gmMVOT4JyV7BP8QDt0XMQ1iZmaBOesZJ/gB9qh4yKuSczUJDhnJfsEP9AOHRdxTWKmJsE5K9kn+IF26LiIaxIzNQnOWck+wQ+0Q8dFXJOYqUlwzkr2CX6gHTou4prETE2Cc1ayT/AD7dBxEdckZmoSnLOSfYIfaIeOi7gmMVOT4JyV7BP8QDt0XMQ1iZmaBOesZJ/gB9qh4yKuSczUJDhnJfsEP9AOHRdxTWKmJsE5K9kn+IF26LiIaxIzNQnOWck+wQ+0Q8dFXJOYqUlwzkr2CX6gHTou4prETE2Cc1ayT/AD7dBxEdckZmoSnLOSfYIfaIeOi7gmMVOT4JyV7BP8QDt0XMQ1iZmaBOesZJ/gB9qh4yKuSczUJDhnJfsEP9AOHRdxTWKmJsE5K9kn+IF26LiIaxIzNQnOWck+wQ+0Q8dFXJOYqUlwzkr2CX6gHTou4prETE2Cc1ayT/AD7dBxEdckZmoSnLOSfYIfaIeOi7gmMVOT4JyV7BP8QDt0XMQ1iZmaBOesZJ/gB9qh4yKuSczUJDhnJfsEP9AOHRdxTWKmJsE5K9kn+IF26LiIaxIzNQnOWck+wQ+0Q8dFXJOYqUlwzkr2CX6gHTou4prETE2Cc1ayT/AD7dBxEdckZmoSnLOSfYIfaIeOi7gmMVOT4JyV7BP8QDt0XMQ1iZmaBOesZJ/gB9qh4yKuSczUJDhnJfsEP9AOHRdxTWKmJsE5K9kn+IF26LiIaxIzNQnOWck+wQ+0Q8dFXJOYqUlwzkr2CX6gHTou4prETE2Cc1ayT/AD7dBxEdckZmoSnLOSfYIfaIeOi7gmMVOT4JyV7BP8QDt0XMQ1iZmaBOesZJ/gB9qh4yKuSczUJDhnJfsEP9AOHRdxTWKmJsE5K9kn+IF26LiIaxIzNQnOWck+wQ+0Q8dFXJOYqUlwzkr2CX6gHTqu2dZ882zv/u2FO3tP/rjiHwU/9AnOWck+wQ+0Q8c105rPP53W7HxDyBQhwTkr2Sf4gXbouGZZ8+jhdMHNl9vOFCPBOSvZJ/iBdui45lhzVaF3nrYP4d/8ev+KJQp+6BOcs5J9gh9oh45rjjUPFh+9P1h/w/Pdafpy8z8PfugTnLOSfYIfaIeOa4Y1l09DLzTmwZWeiIIf+gTnrGSf4AfaoeOaYc0/7007355/06vd6cYvGw8AP/QJzlnJPsEPtEPHNU+HXizMS970F8APfYJzVrJP8APt0HH5PPRKEpyzkn2CH2iHjmuONfff+Xzo4i23Nv/z4Ic+wTkr2Sf4gXbouOZY83Capi/WvoR09P3iDQ/e//4XgR/6BOesZJ/gB9qh45plzf3lt9V/9uSnFwu/P3u0O13paagdyoqYoU/wA+3Qcc2z5sHFn1O6u/1MIRKcs5J9gh9oh45rpjVfP1pv0M9/JmSKkOCclewT/EA7dFzzrfnmt2eP9/a+fvLjVV+2yQ5lRczQJ/iBdui4iGsSMzUJzlnJPsEPtEPHtf01L37qdGHbkd4vwTkr2Sf4gTNEDBed0A79SC9erH930+O9r/15+es5ZyX7BD8wQcQEZ5tpnjWPv6T0ydOTf/dnPa/vnGW4t+oNTBAxwdlmmmXNV7vto4OTF2uyQ6/vnGW4t+oNTBAxwdlmmmPNRWNO02d7/3X5VPSXk7fYodd0zjLcW/UGJoiY4GwzzfUazMsXHXn9cGrVaYde3znLcG/VG5ggYoKzzTTrazAf7bcP5+3Q6ztnGe6tegMTRExwtpnmfe27o/aCTXbo9Z2zDPdWvYEJIiY420wzvwZze05qh17fOctwb9UbmCBigrPNNPfr2B8/KbVDr++cZbi36g1MEDHB2Waa5/Oha69jf7j8upIden3nLMO9VW9ggogJzjbTTF+Xv3Xu327+Pzv02s5Zhnur3sAEEROcbaY51lx+i/3a69gvSvRvkx16Xecsw71Vb2CCiAnONtMsay5fgnmtM1evyGyHXtM5y3Bv1RuYIGKCs800z5r/PP97PJ/v2qHXds4y3Fv1BiaImOBsM8205tGv516n6eiHXTv0ms5Zhnur3sAEEROcbSbimsRMTYJzluHeqjcwQcQEZ5uJuCYxU5PgnGW4t+oNTBAxwdlmIq5JzNQkOGcZ7q16AxNETHC2mYhrEjM1Cc5Zhnur3sAEEROcbSbimsRMTYJzluHeqjcwQcQEZ5uJuCYxU5PgnGW4t+oNTBAxwdlmIq5JzNQkOGcZ7q16AxNETHC2mYhrEjM1Cc5Zhnur3sAEEROcbSbimsRMTYJzluHeqjcwQcQEZ5uJuCYxU5PgnGW4t+oNTBAxwdlmIq5JzNQkOGcZ7q16AxNETHC2mYhrEjM1Cc5Zhnur3sAEEROcbSbimsRMTYJzluHeqjcwQcQEZ5uJuCYxU5PgnGW4t+oNTBAxwdlmIq5JzNQkOGcZ7q16AxNETHC2mYhrEjM1Cc5Zhnur3sAEEROcbSbimsRMTYJzluHeqjcwQcQEZ5uJuCYxU5PgnGW4t+oNTBAxwdlmIq5JzNQkOGcZ7q16AxNETHC2mYhrEjM1Cc5Zhnur3sAEEROcbSbimsRMTYJzluHeqjcwQcQEZ5uJuCYxUzPDOQsXnjB6YILb351DJm77dr0exDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTsQ1iZka7y3kRP7ABBHt0E7ENYmZGu8t5ET+wAQR7dBOxDWJmRrvLeRE/sAEEe3QTrOt+ebZ3v3bC3f2nvxxxT8Kfui9t5AT+QMTRLRDO8205vNPpzU73xAyRfDeQk7kD0wQ0Q7tNMuaRw+nC26+3HamGN5byIn8gQki2qGd5lhzVaF3nrYP4d/8ev+KJQp+6L23kBP5AxNEtEM7zbHmweKj9wfrb3i+O01fbv7nwQ+99xZyIn9ggoh2aKcZ1lw+Db3QmAdXeiIKfui9t5AT+QMTRLRDO82w5p/3pp1vz7/p1e5045eNB4Afeu8t5ET+wAQR7dBO83ToxcK85E1nCd4VnynKJWElXW7bt+v1ID4PlaQs5vhPxf47nw9dvOXWDH+RJG3ZHB16uHgW/8Xal5COvl+84cH731+SsprlUxb7y8+FfPbkpxcLvz97tDv5NFTSmOb5tO/BxU8u353lr5GkLZvpS2evH6036Oc/z/O3SNKWzfftB29+e/Z4b+/rJz9e9WWbJCmNIt/CJUmzsEMlqZ8dKkn97FBJ6meHSlI/O1SS+tmhktTPDpWkfnaoJPWzQyWpnx0qSf3sUEnqZ4dKUr+xO/RafvGWpOux7UK5FDNVlATb8SPyExoxAj8hNCIzVZQE2/Ej8hMaMQI/ITQiM1WUBNvxI/ITGjECPyE0IjNVlATb8SPyExoxAj8hNCIzVZQE2/Ej8hMaMQI/ITQiM1WUBNvxI/ITGjECPyE0IjNVlATb8SPyExoxAj8hNCIzVZQE2/Ej8hMaMQI/ITQiM1WUBNvxI/ITGjECPyE0IjNVlATb8SPyExoxAj8hNCIzVZQE2/Ej8hMaMQI/ITQiM1WUBNvxI/ITGjECPyE0IjNVlATb8SPyExoxAj8hNCIzVZQE2/Ej8hMaMQI/ITQiM1WUBNvxI/ITGjECPyE0IjNVlATb8SPyExoxAj8hNCIzVZQE2/Ej8hMaMQI/ITQiM1WUBNvxI/ITGjECPyE0IjOVJOVgh0pSPztUkvrZoZLUzw6VpH52qCT1s0MlqZ8dKkn97FBJ6meHSlI/O1SS+tmhktTPDpWkfnaoJPWzQyWpnx0qSf3sUEnqZ4dKUj87VJL62aGS1M8OlaR+dqgk9bNDJamfHSpJ/exQSeo3doce/fDpNO18/vO2c/yF148WEac7T7ed4wP2py+3HeE9fr2f4fEDP4BvUxxC8K08dIe+/mo6dvfltqO8z0FLOH3yy7aj/JXDCVoBR9/hL/EK9gFcSnAIybfyyB36572TszHd2naW9zg9vdN0k3c4Th3uUitgH3+JV7gP4NsUhxB9K4/coYv765N/P36qsvPttsNc6tXi1rr7xyLi9xP4Hnv7fJcab/kAfvGSfIlXuA/g2xyHEH0rD9yhi/923Tj+2GTxH9oHWw5zuYPTQ3vIfQ7w+tHqv//Iu2v/JNcB8QlKQ34A36Y4hOxbeeAOPVw/G8wDvH9yNN4ePTz9R5iDxdOUT/6D+Qie3Vvcxw/9AC4lOITsW3ngDj2zD/wA4KJ96PFdPnh/f0k8um9XH4aePPskPkE5Rn4AL8AewlPEW7lAh/7+CPxx3gnsU4C3+8vPlUEr4PCsOA+5HQp+AM/jHsKGeSuP3qGrL+jt/GPbMT7okHg4zkArYO3J5+IpKTHhCegDeB77EGJv5dE7dPlFx+XHUtvO8QGL88H7GGUNtAIOzh41O/SjwQ8h9lYevkNvf3Yb/c3DK4sPoti3GLQC9s91KPg5FPUBXEc/hNhbefQOXTrap37PRrM8veiA1AqwQ+PwD+Fb6K08Woee/EDDuc+NL48H5wsO70Rc/hwb6mC8+yBCK8CP5cPgDuHlWLfysRIdyjrBFyMuf4jlFur0JupQv6YUg3cI3wP4QNboUNQHehciHvB+hCVNh6b43qYV6AN4AngI3wN1Kx8brUMvB36SsvwJ4G+2HeKDoBWwdl0P0F9Tpj6ATY5DuAK8lQfu0LUP9A6wJ3j5YgrE10S8AFoBiyfM7XN49G8Phz6Ax/CHkH0rD9yhZ6+gsPhvF/RJykGKT+RzKyDFa44sUR/AJf4hZN/KA3fo8kt4n/y0fAXsXeoNdvY8Co5aAavXbeO/9h33AXyb4hCyb+WBO/T4BxvQry279uq3E/prItgKSPIazNwHMMchRN/KI3fo2SPPe9xXlv95xR/fFWwF+LtAPlaOQ0i+lYfu0ONfZMX9XVtrv+EAfHyXuBWQ5HfScR/AJIcQfCuP3aGSNC87VJL62aGS1M8OlaR+dqgk9bNDJamfHSpJ/exQSepnh0pSPztUkvrZoZLUzw6VpH52qCT1s0MlqZ8dKkn97FBJ6meHSlI/O1SS+tmhktTPDpWkfnaoJPWzQyWpnx0qSf3sUEnqZ4dKUj87VJL62aGS1M8OlaR+dqgk9bNDJamfHSpJ/exQSepnh0pSPztUkvrZoZLUzw6VpH52qCT1s0MlqZ8dKkn97FBJ6meHSlI/O1SS+tmhktTPDpWkfnaoJPWzQyWpnx0qSf3sUEnqZ4dKUj87VJL62aGS1M8OlaR+dqgk9bNDJamfHSpJ/exQSepnh0pSPztUkvrZoZLUzw6VpH52qCT1s0MlqZ8dKkn97FBJ6meHSlI/O1SS+tmhktTPDpWkfnaoJPWzQyWpnx0qSf3sUEnqZ4dKUj87VJL62aGS1M8OlaR+dqgk9bNDJamfHSpJ/exQSepnh0pSPztUkvrZoZLUzw6VpH52qCT1s0MlqZ8dKkn97FBJ6meHSlI/O1SS+tmhktTPDpWkfnaoJPWzQyWpnx0qSf3sUEnqZ4dKUj87VJL62aGS1M8OlaR+dqgk9bNDJamfHSpJ/exQSepnh0pSPztUkvrZoZLUzw6VpH52qCT1s0MlqZ8dKkn97FBJ6meHSlI/O1SS+tmhktTPDpWkfnaoJPWzQyWp3/8HyS34LEd3gjcAAAAASUVORK5CYII=" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTBdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0wXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==0]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTFdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0xXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==1]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDM1MClcbmhpc3QoTTBfbWNbd2hpY2goKE0wX21jPnhsaW1fQ0VbMV0pKihNMF9tYzx4bGltX0NFWzJdKT09MSldLDFlMyx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE0wOiBHLWNvbXB1dGF0aW9uXFwpXG5gYGBcbmBgYCJ9 -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M0: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNcl9tY1t3aGljaCgoTXJfbWM+eGxpbV9DRVsxXSkqKE1yX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTXI6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Mr: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNMV9tY1t3aGljaCgoTTFfbWM+eGxpbV9DRVsxXSkqKE0xX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTTE6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M1: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIC0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS1cbiMgLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLVxuIyAtLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tXG5yaG8gPSBcXHVuaWZcXFxuUE9TVHJlc3VsdFJob1VuaWYgPSBFRFBtZWRpYXRpb25QT1NUKE1DTUNyZXN1bHQsIGVzdHR5cGUsIHJobywgc2F2ZV9jbHVzdGVyKVxuYGBgXG5gYGAifQ== -->
```r
```r
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = \unif\
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Tue Feb 21 18:55:31 2023 Post-Processing 10 ( 20 %) Time: Tue Feb 21 18:55:32 2023 Post-Processing 15 ( 30 %) Time: Tue Feb 21 18:55:32 2023 Post-Processing 20 ( 40 %) Time: Tue Feb 21 18:55:33 2023 Post-Processing 25 ( 50 %) Time: Tue Feb 21 18:55:33 2023 Post-Processing 30 ( 60 %) Time: Tue Feb 21 18:55:34 2023 Post-Processing 35 ( 70 %) Time: Tue Feb 21 18:55:34 2023 Post-Processing 40 ( 80 %) Time: Tue Feb 21 18:55:35 2023 Post-Processing 45 ( 90 %) Time: Tue Feb 21 18:55:35 2023 Post-Processing 50 ( 100 %) Time: Tue Feb 21 18:55:36 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc
CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c(\NIE\,\NDE\,\ATE\)
NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE
q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col=\red\,ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col=\blue\,ylim=ylim_CE);par(new=T)plot(sort(ATErhoUnif),col=\green\,ylim=ylim_CE)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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mMP5CSpho7P5ccNtbcJyEdK10NHD1ZHvtDnKQEZSaqh/+c3+Uw6IC9J7A/d8kRdzi/zDGYgIyncpzT1qa+czj9fcmrqNvNQIH3J3C9/+YTPlweKFruhV33JqRnzUKAwS9jbtFIaCsQUe2+T+5SAksVt6LMnq88d8A0CaCgQU+RnMD9RVW94dMC36ExDgZjiPftu7Gt+5Q2T9fhrbvjln/97rSkB5Vnq58vb2wQUJvY8dGJa0Ktebx4KFGZJn+v5/EMnq5UsL2koENPSPhv52XFE3zrgm7WkoUBMy/t8+QdXMhHVUCCm5TX06ZV8tpKGAjFFXVOauf3+T4xP5q3LA4VZ3t6m29+koUBpljIPtT8UKNQy9za5HgqUZql7m36BhgJlWVpDr/yFqvqlnX/LzTfe0uA154c5JoCeltXQKw+Nz+U/u/M8dO+niUwdPTvIMQH0Fauhz1+Y8+QjP3gycE3pgxsaCqRric9tujloXf6ZjerI6z6y20eDjglgcEtr6Ev+zj1he5vGEb2u/fXPA44JYHCRGnrlPadn7n/kkfd/sl6YD9vbdLGqbhrimAAGl8P98meqI3cH/cKRhgJxLW9v0wNV9Y1hv+/lE9XxsF+poUBcy9zbFPw5yY/d8kXtrog2rOEHviVAG9H3Nv3Uv/qKOmX1FqXAaehgxwQwtCXubfoNy7/TU0OBuJb5uZ4r+CgQDQWiiru36btPVNVnfWu9t+nJe3s/+m7zQ+94Z+eNohoKxBR3TemJ2X6mHuvyWy6f6HKT58JjAhhO1IbW3dw5ge/9eUoaCiQnakNfmL+984XAez13aCiQnOgN/bGHJx8Fcur+n9ZQoDixG3rVF26vyn9G2HObZjQUSE7cNaUHJ/U8durU5PGhrocCpYnb0P89DucvfrT+6rm/Mv7yd/T67TUUSE7chv63ehb6vePZ55WP1TPRP9Drt9dQIDnR9zbN89nIQGFirym96Ju3A/o539T3RqVBjglgQPH3hz7/8JtPnbr9/k/03h86zDEBDCh2Q2fPDH32pIYCpYm+t2nnHvknXA8FihO3oU/XD6+fPo75f/6eqvr9A75Z8DEBDCduQ/cszDuXBwoTuaE/oKFAyaKfy+/4rG89/RbXQ4GyRN9jf/2Frb1NA75RBxoKxLS8vU2roaFATMt7BvNqaCgQU+xz+XFDdz5q/sIKzuc1FIgp+mfS3WxdHihX3IZ+6qS9TUDJlrC36ctOb7O3CShMpIa+cN+psT/yBdP550tOTd1mHgqUJVZD76kaOJcHChN1Hvo1N1dXfcmpGfNQoDBL2Nu0UhoKxBR3Tek/VNVbB3yDABoKxBT9fvnPXv5a/DwNBWKKfa9nVV3/6IBv0ZmGAjFFXVP62pvtbQKKZm8TQLio89BTX/el1ZHP/332NgGlirum9J7T9zqXBwoWd03pTc7lgaJFbeinvrK66ovdpwSUy3PsAcJpKEC4uPd6PuheT6BocRt65aHq2P0rvdlTQ4GYIjX0ynvqh9bv2tv0tTdXR88O+G6djwlgcPHuU3rxB/bdraShQGHiNvS+evZ51etPmYcCZYra0PkvVrRIr6FATBoKEE5DAcJpKEC4SA391Mnq2A/VX8zKefmENSWgNJEauhPMnZhqKFCg2A2dlVNDgfJoKEA4DQUIp6EA4SI29B9fGPvx7S8mX2koUJZ4DW2goUBhNBQgXKSGfvpkdfRPnR777hNbX9RfHfvhAd+t8zEBDM69ngDhNBQgnIYChIvY0PdfuPBT//HvnqiO/sk//68vXLjwpIYCxYnX0AYaChRGQwHCRfts5L/2VXU1f+5v/ZZv+ZY/ccvN9dc/7zvesvyPmtdQIKZIDR2NHhxX8/pHt3/03APjH37ugO/VloYCMcVq6LMnq+ob5//hE1V17H0DvllLGgrEFKuh42Rev+vM/coDe6K6HBoKxBTreui4mG/d/U+fXsnJvIYCMcVr6N4z9/HZ/fXWlICyxPtcz61HjeyonznyQwO+W+djAhicZ98BhNNQgHDx7lP6zH97YZeffJP7lIDSxH5u04EvLYGGAjFpKEC4uM++m+fZd0B5PLcJIJx1eYBw8T7Xs4HP9QQKE+tc/r5TeziXBwoU7fmhu115qJ6Gfu+Ab9aShgIxLaehz96764nMS6ShQEzLaOjKJqEjDQXiWsL10D/8K8YJ/TlfPP7qNtdDgbLYHwoQLvY8dGcSqqFAgeJeD73yI/WV0Ps/aV0eKFPUhj5XL8e/9FHr8kCpYjb0v9c3K33DCiehDccEMKR4Dd2ZhO58EewjHzk/+8HmG295zfnFP/fAYwIYVrSG7kxCJ5dE/1b473rpzno56tq7tn98+USXZ5doKHCAq2t9foOIny9fHXvvhQv/69vHX/yifzN9hOgnAn7TZza2NkZdtzX51FBgKFfPfRsm9f2hk4foveKW31JPRc9uv6KhwBCu3vN9gNQbeq6qjtw9/v7SHduPH9VQYBhXN3zVVaxz+fecPn36z9087uav+47TO97yya6/5eY4nTdNvzqzdTqvocAwEm7oaIjl+NEkmJNp6Gga0eMjDQUGcvWCrzuJvi7fz3wwt+akGgoMIuWG7qzL79J9XX5XMKeTUg0FBpFyQ5s/k26ypvSxP9hhZWk899w+lx+7WK8raSgwjISvhy5s6JP3dludPze9CDr70XX/RUOBQSTc0Cv/4quq6rP+6Ond3vKf762q6ztdI6232H/e7NbOcUSv6fQZyxoKLJTu/tCxj9WLSm94704xn//4fSGPHhlXc76Z9Q8XN7Rh7tvx7YBSNd3Wmex9SrXJ45rGXnLq9jef+urp11/ffaH+gxu7mvnYhnko0F1zLlO9X37qykMn56eE9cOYA2w+vus5TZvft6GhQEcDnLY3inWv53dunbM/94OnJh09dtvf3Npu32ldfshjAtbXEMtHjeLdL//S9zf9nK7r8nM2P/SOd7Z/cOj+YwLWV24NnWyyf+l79/6Mj3del5/TbWNowzEB62qQ7fSNlrku/5dD1uVnNBQIlGNDh1qX36GhQKAsGzoaffqbdu/VfNEP9/ntNRRoZ/+Opfyuh9bPGHnynupFf/0rvrzO58/+nX886BnMczQUaKVhK2h2DX32ZLVf8HLShIYCbTRuBc1sf+ho9MT+hB57X6/fXkOBFhZMOfvf1tkoWkNfeM/p028+WR27fet5I/c/8siFC71+ew0FWlh02t77ts5GUdeUdlXvygM9z+WDaCismXhL8I2iNvRTJ6pjP7T9gxfu6bmmFERDYc0U0tDJuvxPnqyO/qPtDwJ5qO+6fO9jAtZAIQ2NsC7f+5iAdRBtG1OjjNbl+x8TsAYKaehkXf5EVf362br88mehGgprKNZW0EZR15ReuCf4wctD0VBYP5G2gjaK2tDNk1f95ulTR6Zus6YELEGcraCN4j5zZM/CknV5oDCx99hf9fpTM+ahQGFiXw9dwdRzFw0FYora0NGDVfXWAd8ggIYCMcVt6JWHrMsDJYv7+fLvOX3v1nLSDb/md7seChQn+v5Q6/JAPEvcxdQsbkPv+0N1Oo/ccMNG/f2vNQ8FBrXM3fTN4l4PrSeiL320/uq5e1cyDdVQKNlS7+psFrehT8ye1XTlgar6xgHfrCUNhVIs8cM6O4i7pvTA3N6mpz37Dgi3zA/r7CD6Hvsfe/hUfS301P0/7Tn2QLCG0/YlP225WeyGHj2xvSg//kpDgTBNU861aOjk2cunTp20twnoYT0bWt/rObcu73ooEKY5l8VfDx3916r6jL8//fL/fmFV3TTgm7WkoVCCNW1ovS5fHfve8ezzysdOmocCoRactpe+P9S9nsAwFkw5C79PadzQF33zdkA/55s0FAi06LS98Pvl76mOve/5h9986tTt93/i2ZMaCoRK4LS9UfR1+Z37O59wPRQIt/rT9kZxG/p0NZ6ITr8cT0PdLw+00niGvvLT9kaRn2P/wNa6/P/7dydWMg3VUMhQolPORnEbOpl9bvtZf2/A92pLQyFtDbPLVC99Norc0CfmtzZ97oDv1ZaGQtISfRpTe3EbWq/Fv//hv/oFVfUb/9PJlXzGp4ZCKpquZzZNOTV05onq2Hu3nxz69EomohoKiWi6yJnsk0Tai32vZ53NJyb1HM9J7W2CtdV4kVNDD/69Xrin3s5UL85/zyOP/KhnMMP6amxkYy41dGbc0O/5l58cT0CP1EtKN2sorK32DXU9dKZ+5siLP/C0Z47Amtm3fHT4mpGGNl0P/Wd1N+sHMVff8PGTVfULXQ+FdbB/+eiQZ9c1/4QcEhp5Xf5cdeSun5g+OfTKP62qXzLgmwUfExBZ+4+PS/aJdu3FnYf+wM72+smjRK3Lwxo45NJn4zn+3juVkrw1vlHs66Eb04a+ddJQ10NhDXRpaFZTzkaxG/q3Hz79N768Ova+F77zj71JQ2ENdPzYjoymnI2WsD90epvSyDOYYS0cvJSUcy4bLeE+pQenN3k+7XoorIOFe+Rzn3E2i3+//E9MHzZS363kGcywBvLa39lX9Oc2VdP1+Ol2+wHfLPiYgLg0dMDf6+k6ovXHgUw+nm7A92pLQyGu3J+h3Ffkho6ef/j0/fVV0Be+8+tX8EkgGgqRNa4UFbp81Ch2Q1ctxWOCcuS/R74vDQWCrdelz0YaCrS0f3apoRoKtNT6aUxrRUOBVto/jWmtaCjQRgEffRSFhgJtdHoa0xrRUKCFEj62IwoNBVro+ES79aGhQAtr9kS79jQUaGPhg+jX55akRhoKtOHSZzMNBVpx6bORhgLtrP2lz0YaCuut8Xpm80XOdb/02UhDYa2t/fM/+9JQWGeNFzld+exAQ2GNuYGzNw2FtdHy+Z8a2oWGTj1Vi3oksGotn//pYUydaOjEU3PfQpnaPv9TQzvR0NpTe76H3LU7bdfQ/jR0NJ9OEaUMDZuT2l/6dD20Cw0daSjFaf2xHRram4buDqeIUoAOH9thf2hfGqqhZK7Hpc9R41m/+5S60FANJW9tP7G40/M/3RnfmoaOXA8lZ/0ufdKbho40lIz1vfRJXxpasz+UXHVZWHeVMwYNnXCfEjk4aPUo+NIn/WTU0M3HX33DDa98V7df5H55ynHgxnmn7SuSQUM//MZb7hp/98xGNXHtuxM4Jli+pjD6xOKVS76hm3fU4bzu/OUT1ZYjd6/6mCC6lo+pc9q+cqk3dJrQqjp+pqpuPD8aPb5RB3W1xwTRtb3f3Y6llUu9oRfH887XfeSxOqM3TV6o56O3rvaYILbWmz5d+ly51Bt6ZtrO8XdHz05fGVf1+GqPCSLrcq+mS58rlnhDx6fyk8ufz2zshHP85XZOV3NMEFunhrr0uVqJN3R85j4J5vj743teWtkxQWTu1cxJPg3dXknSUEqnoTlJvKH1svyeFaSLnRbmNZT82Difk8QbOjpX7Zl11lW9qf2v11Ay5H73jKTe0DqZR26czTsff9XeqC7/mCAyG+czknpDR5d3RbPeHXrAfUrVfjGOCSJz2p6P5Bs62vy+jV0Ndb88a8BpezbSb+gum/+gU0E1lFw5bc9FZg3tLMVjYn357KLyZNTQzQ+9450dnjYypaFE1z6MPkOzQBk1tNvm+i0aSqDWZWwfxsaVIstHmdNQaNK6jO3D2OWjj8iGhkKD1mXsEEYNLZKGwn7tcxfy4tzXi5/GRCY0FPZrXcYOYdTQMmko7NM+dxq69jQU9onSUNdDy6ShsE/Q7NKa0nrKqKFBUjwm0hdjTcn+0DJpKOwXMLtsE0b3KRVIQ6FBhzJ2CaP75cujoay9vre2C+Na01DWSev73ZWRljSUNdL6fndoS0NZH63vd4fWNJS1YX8mEWgoa6P1/e7QnoayLtyvTgwayrrQUGLQUNZFh/vdoTUNpVD7t3JaUyICDaVMDVtBO9zvDm1pKEXqe787tKShlOjAh8+1ut8d2tFQctKcu5aXPhf+eginoWRkwTxy36t2LLE0Gko+DrqeuWCxXUOJTEPJRvtPKdJQlkZDyYZPeiNBGkouDn9inbuPWD4NJRddGmrnPMuioSRq3zakTg21c54l0VDS1PleTVtBWQkNZfUactf+Yztc+mSlNJSV6/l4EJc+WSUNZal6TTlb36cES6OhRNL8+exz3+56adFXe39yy/vlYVk0lP6aGtY4OWw75XSfEdnQUHpryuWBz+88NJcaSjY0lL76LaG7z4i8aSg9tb9fvcOUU0PJhYbSU8jksv2vklASp6F00u4OzAEeD2LDEnnQUBZpt9reZU2o05TThiWyoKGM2m9Oashd3zWjBe8EmdDQNdN253v71fb2L5pyUiANXS+9dr53yeWiWja9CBnT0HK1vDW9fRkPucrZNI/dP+U15aQsGlqshoj13Pl+8FLSvuupask60NAi9HkaUvtcLmqoXLLGNDQ3LZfQe+58d/cQtKOhmemzhN5757uGwl4ampdeueyy873TajusLw3NSs8l9JApaavVdlhbGpqVnlPOTjvfrbZDCxqak9657LTzXS7hcBqak6GmnHa+w1A0NCdDTDnVEoakoek6YON8mx1Hln9gCTQ0WQftBDXlhERoaKoOWiy34whSoaGJWnRLkCV0SIqGJmrhbZVyCSnR0DQtfEQSkBQNTZOGQh40NE0aCnnQ0ER5zBxkQUMTpaGQBQ1NlUd1Qg40NFk2zkMGNDRddoJC+jQUIJyGAoTTUIBwGgoQTkMBwmkoQDgNTYJtTJApDU2B7fSQKw1dtgM+aU5EITsaumQNU06PF4F8aehyNU05NRTypaFL1ZRLj1uGjGnoUmkoFEZDl6kxlxoKGdPQiPYtwR92FVRCITcaGs/+JXgNhdJo6CCa7jNqvwRvfyhkS0OH0HSfUWMuF0w53acEucqqoZdffcPLz3b7JUtpaOM8stOU0/3ykKm8GnqiOppgQw+ZcTZ9rZdQCA3tr1NDTTmhKIk3dHz2PudlVVVdM/6+wwn98MfUecOSWScULPWGnqgadJiMDn5MbTcs2bEEayHxhm7ekVhDG9aENBTWWOINHY0+uFEduWvr69VfD+2+YUlCoWjJN3R06VVVdeP5yZd5NRx8GZoAAApjSURBVNQSPKyB9Bs62nxbVV377vqrlTf0kNP2fXcqWYKH0mXQ0NHosfH5/OtG6TbUjBPWVhYNHV26o6peeT7dhppxwrrKo6GjzbdX1ZG7Vt5Qi+3Abpk0dDR6ZqOqXnFYQxv2QQ17FBoK7JJNQ0ebd3bcGjqxhP2hwBrLp6GTpaWVN9TyETAvp4aOLr3xltec7/ZLlnC/PLDGMmro5ofe8c6OBU3zudBAOTJqaMCqvIYCcWkoQDgNBQinoQDhNBQgnIYChNPQA9gKChxCQxdzSxJwmIwaGqTHMbk1HjiUhi7iEU3A4TR0EQ0FDqehCyx8ZD3AjIYuoKFACxq6gIYCLWjoIq6HAofT0EU0FDhc8Q0FiGnIXg34e8WUy3F2UuKgShxTkYMyprzftbtcjrOTEgdV4piKHJQx5f2u3eVynJ2UOKgSx1TkoIwp73ftLpfj7KTEQZU4piIHZUx5v2t3uRxnJyUOqsQxFTkoY8r7XbvL5Tg7KXFQJY6pyEEZU97v2l0ux9lJiYMqcUxFDsqY8n7X7nI5zk5KHFSJYypyUMaU97t2l8txdlLioEocU5GDMqa837W7XI6zkxIHVeKYihyUMeX9rt3lcpydlDioEsdU5KCMKe937S6X4+ykxEGVOKYiB2VMeb9rd7kcZyclDqrEMRU5KGPK+127y+U4OylxUCWOqchBGVPe79pdLsfZSYmDKnFMRQ7KmPJ+1+5yOc5OShxUiWMqclDGlPe7dpfLcXZS4qBKHFORgzKmvN+1u1yOs5MSB1XimIoclDHl/a4AZdBQgHAaChBOQwHCaShAOA0FCKehAOE0FCCchgKE01CAcBoKEE5DAcJpKEA4DQUIp6EA4TQUIJyGAoTTUIBwGgoQTkMBwmkoQDgNBQinoQDhNBQgnIYChMuhoY+/uqqql9+16sMYzpnqptkP8h/dpTtftmcI+Y9ptPl940EdeeW7Z68UMKja5h3V8Z0fZD+mZzaqbdt/ppY+pvQbuvm2rX9HN55f9aEM5OLsv3cJozu3/T/xtWenLxQwptGlV+0ZQwmDmjhT7TS0gDFd3Eno1p+pFYwp/Yae2fmXdPzwn5yDixtzDc1/dOdm/xdfN/3fNv8xjS6f2DuGAgY1cXFuBAWMae7/vumfqRWMKfmG1pP1zzs/+evlyN2rPpghPLYxd96R/+jqEdz40fHf/2/fHlb+Y5r8Sbz2z4zmxlDCoGqTvxy26lLCmM5UR8/O/3gVY0q+oWe2g3Mu478tZy7dOfd3ZgmjO7czmItbE9H8x1SXZuuP5ngMt9bfFzCoiTO7p9a5j2nzju2Tny2rGFPqDZ393zz+17X7r5wcnRv/NXntP9zJTgGjm00EtoZQwJjmrlhvfVXCoGrnqiN/emMrLiWMaTztvGn+xysZU+oNfWZj56+T7SlBzs5UR157fvYntKzRTXNa2pgmp4SFDKpOzs5QShjTxT0HvpIxpd7QuX9Je/995ehMfelw1yynnNFt/c1f0pg+fOfWGWEZg5psa9rJTAljGs+r737sZVV1zWunZ/QrGVPqDZ3722TvvD1bs4YWNbqL094UM6bJ8suR3z75uoxBTU4UdhpawpjGpwkvm67CT1eQVjKm9Bu6s7yW7X/oveYbWs7oxsmZDKaYMU22bx+ZTnCKGNR0ZjbX0OzHNLcFbYX/86Xe0DO7/qVkunq4x6yhBY1ufJ44HVUxY3rmhlfcUG3dOVDCoMbBqQ985/gLGNP4uI+8tt5YV28YrBfoVzImDV2+EhtaJ3S6y6ScMY1tnlnhn82Bbe2gKKmhM5emZ0Ea2qCAE459CjyXr2+N3NqoV8yYJuq/G24tYlDnZncLFHMuP2e6T9m5fIMSLnzvVd6aUn0qdXxrr3MpY9pycevPZu6D2jnsotaUZqbDsqbUoIQNGHsVt7fp3NydV6WMadv0z2b+g5q7sXzrRrn8xzRvhf+dUm/o3N8m55Z3B2xcu/bYFzC6+t7k1+38qIwx7ZgOJ/9B7W9o/mOad3F1Y0q9oZdPbF9ny/eGtL0uzt/rmf/o6udzzD1ms4QxzZ0STq+z5T+o/Q3Nf0zz/53OTL5cyZhSb2gJD0bY62JJzxypj3z1j30Y2MWdMdW7Z+rpTAGD2jJbr85/TLP/TuOvjk43oXnmyD6TZ6tl/oCuPeYamv/oZn/zb8t/TJPV+GvfVT/MfmPrj2IBg9oya2j+Y9r132nnwYvLHlPyDS3hQbF7zD/HPvvR7T5H3H5OXN5j2vURE+U8WHpqbt9k/mOae4z96v47pd/QAj6wYI+SPgukngnsbWjuY6rtRPS60j4LZK6hBYzpsQT+O6Xf0AI+OGuP+YbmPrr5O5arnSv8eY9pYvKZdKV90F5t1/07+Y8pgf9OOTQUIFUaChBOQwHCaShAOA0FCKehAOE0FCCchgKE01CAcBoKEE5DAcJpKEA4DQUIp6EA4TQUIJyGAoTTUIBwGgoQTkMBwmkoQDgNBQinoQDhNBQgnIYChNNQgHAaChBOQwHCaShAOA0FCKehAOE0FCCchgKE01CAcBoKEE5DAcJpKEA4DQUIp6EA4TQUIJyGAoTTUIBwGgoQTkMBwmkoQDgNBQinoQDhNBQgnIYChNNQgHAaChBOQ0nc5RPVded7/xSIRENJnIaSNA0lcRpK0jSUxGkoSdNQEqehJE1DSZyGkjQNJXHbgZx8f+nVVVW9/K7tf3bpzo2quvH8rKGTF6557eQHF6vq6Nn6i807qur4Kg6ddaChJG6+oW+vpraKeG76o6P/ZLuhWy9UR26tf3Rm6yeOXzVNJRYNJXFzDZ2ZNHK7mNU1G9OfsvNCdeTurV8x/onPbEx/CDFoKInb1dBXvns0enxjOr8ct3H641dV04nm9guXXrU18Zyczddn8jeteAwUTENJ3HxDp+fwz0ynnee2f1xXsn5hfO5+4/SFM9OZ6iSfzuSJSkNJ3FxDt07Jx2k8erb+dvsU/eIkk9OXJ8aVPb71/TWVM3li0lASt2tdfvLKNJZzG5qmX46/Pb7n10yvkDqTJyINJXEHNHQ7meMXxv+ovhw6M/2526f5EIuGkrheDa1fcypPTBpK4lqfy29fBJ1TT0NNRIlKQ0ncoobOrSlNF+ob7vi8WFXHz7ggSkwaSuIWNXR2+9Hc3qatWm5NSce/5OhZW+yJSkNJ3MKG1htGr333aPThvXvsNx/byuY0qjaIEpOGkriFDa3P1Kd+/om993pOpqHTbaOTaeqtKxwAZdNQEre4oaPHNvY8c+Rt2wm98fzcpvydBzjB8DSUxB3Q0Omj7l6599l3R17+rvrrMzvPdzrj2XdEo6EA4TQUIJyGAoTTUIBwGgoQTkMBwmkoQDgNBQinoQDhNBQgnIYChNNQgHAaChBOQwHCaShAOA0FCKehAOE0FCCchgKE01CAcBoKEE5DAcJpKEA4DQUIp6EA4TQUIJyGAoTTUIBwGgoQTkMBwmkoQDgNBQinoQDhNBQgnIYChNNQgHAaChBOQwHCaShAOA0FCKehAOE0FCCchgKE01CAcBoKEE5DAcL9f9ojjixVbvieAAAAAElFTkSuQmCC" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuQ0VfdGFibGVSaG9VbmlmXG5gYGBcbmBgYCJ9 -->
```r
```r
CE_tableRhoUnif
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estimates sd quantile025 quantile975 CIlength95NIE -0.08813969 0.4259925 -0.4147857 0.2832588 0.6980446 NDE -3.10589206 0.6500578 -4.1201645 -1.9771476 2.1430170 ATE -3.19403176 0.5405245 -3.9885375 -2.0161597 1.9723778
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\newpage
### dist. of f(M)
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<!-- rnb-source-begin {"data":"```r\n```r\nset.seed(1)\nM = LITEdata$att\n\nYY = c(Y,Y+rnorm(N,0,0.1))\nMM = c(M,M)\nVV = c(V,V+rnorm(N,0,0.1))\nZZ = c(Z,Z)\n\np_C = ncol(C)\np_C1 = sum(apply(C, 2, function(x) { all(x %in% 0:1) }))\np_C2 = p_C - p_C1\nAA = rbind(C,C)\nAA[(N+1):(2*N),((p_C1+1):p_C)] = AA[(N+1):(2*N),((p_C1+1):p_C)] + matrix(rnorm(p_C2*N,0,0.1),ncol=p_C2)\nCC = AA\n\nMCMCresult = EDPmediationMCMC(YY, MM, VV, ZZ, CC,\n                              gibbs_iter, gibbs_burnin, gibbs_thin,\n                              D, num_MC, num_MC_prior)\n\n{\n  # Significance Level alpha\n  level = 0.05\n  quantile_alpha = c(level/2,1-level/2)\n  \n  # the number of Gibbs Sampler stored\n  n_MCMC = MCMCresult$constants$n_MCMC\n  \n  # Define interation check\n  iter_check = floor(n_MCMC/10)\n  \n  M0_mc = list(NA)\n  Mr_mc = list(NA)\n  M1_mc = list(NA)\n  \n  N = MCMCresult$constants$N\n  D = MCMCresult$constants$D\n  num_MC = MCMCresult$constants$num_MC\n  p_V = MCMCresult$constants$p_V\n  p_Z = MCMCresult$constants$p_Z\n  p_C1 = MCMCresult$constants$p_C1\n  p_C2 = MCMCresult$constants$p_C2\n  \n  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc\n  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc\n  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc\n  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc\n  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc\n  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc\n  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc\n  \n  a_Ysig2 = MCMCresult$priors$a_Ysig2\n  b_Ysig2 = MCMCresult$priors$b_Ysig2\n  a_Ybeta = MCMCresult$priors$a_Ybeta\n  B_Ybeta = MCMCresult$priors$B_Ybeta\n  a_Msig2 = MCMCresult$priors$a_Msig2\n  b_Msig2 = MCMCresult$priors$b_Msig2\n  a_Mbeta = MCMCresult$priors$a_Mbeta\n  B_Mbeta = MCMCresult$priors$B_Mbeta\n  a_Vsig2 = MCMCresult$priors$a_Vsig2\n  b_Vsig2 = MCMCresult$priors$b_Vsig2\n  a_Vbeta = MCMCresult$priors$a_Vbeta\n  B_Vbeta = MCMCresult$priors$B_Vbeta\n  a_pi   = MCMCresult$priors$a_pi\n  b_pi   = MCMCresult$priors$b_pi\n  a_mu   = MCMCresult$priors$a_mu\n  b_mu   = MCMCresult$priors$b_mu\n  a_tau2 = MCMCresult$priors$a_tau2\n  b_tau2 = MCMCresult$priors$b_tau2\n  \n  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws\n  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws\n  \n  rho = runif(n_MCMC)\n  \n  # End initial values ------------------------------------------------------------\n  for (post_reps in 1:n_MCMC) {\n    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]\n    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]\n    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]\n    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]\n    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]\n    \n    rho_mc = rho[post_reps] * rep(1,D)\n    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]\n    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]\n    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]\n    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]\n    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]\n    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]\n    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]\n    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]\n    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]\n    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]\n    alpha_theta = alpha_theta_draws[post_reps]\n    alpha_omega = alpha_omega_draws[post_reps]\n    \n    MCresult = EDPpostmc_concon(p_C1, p_C2,\n                                n_k, n_rk, Ky, Kyx, max_Kx_Sy, \n                                D, num_MC, rho_mc,\n                                YbetaPars, Ysig2Pars,\n                                MbetaPars, Msig2Pars,\n                                VbetaPars_array, Vsig2Pars_array,\n                                ZpiPars_array, XpiPars_array, \n                                XmuPars_array, Xtau2Pars_array,\n                                alpha_theta, alpha_omega, \n                                f0_z0_mc, f0_z1_mc,\n                                YbetaPrior_mc, \n                                MbetaPrior_mc, Msig2Prior_mc,\n                                VbetaPrior_mc, Vsig2Prior_mc,\n                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,\n                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,\n                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,\n                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)\n    \n    M0_mc[[post_reps]] = MCresult$M0_mc\n    Mr_mc[[post_reps]] = MCresult$Mr_mc\n    M1_mc[[post_reps]] = MCresult$M1_mc\n    \n    if (post_reps %% iter_check == 0){\n      cat(\\Post-Processing\\,post_reps,\\(\\,(post_reps/n_MCMC)*100,\\%)\\,\\Time:\\,date(),\\\\n\\)\n    }\n  }\n  \n  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)\n}\n\nM0_mc = unlist(distM$M0_mc)\nMr_mc = unlist(distM$Mr_mc)\nM1_mc = unlist(distM$M1_mc)\n\nmean(M)\nmean(M[Z==0])\nmean(M[Z==1])\n\n# n = MCMCresult$constants$D\nn = 1e5\nylim_CE = c( 0.0, 2.0)\nxlim_CE = c(min(M)-1, max(M)+1)\n\n# print(\\dist. of M based on the data\\)\nplot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\\\,col=\\red\\);par(new=T)\nplot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\\\,col=\\blue\\);par(new=T)\nplot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\Data\\,col=\\green\\)\nlegend(\\topright\\, legend=c(\\M\\, \\M[Z==0]\\, \\M[Z==1]\\), col=c(\\red\\, \\blue\\, \\green\\), \n       lty=rep(1,3), cex=1, text.font=4)\n\n# print(\\dist. of M based on the G-computation\\)\nylim_CE = c( 0.0, 2.0)\nplot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\\\,col=\\red\\);par(new=T)\nplot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\\\,col=\\blue\\);par(new=T)\nplot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\G-computation\\,col=\\green\\)\nabline(v = 0, col = \\black\\, lwd = 2)\nabline(v = 1, col = \\black\\, lwd = 2)\nlegend(\\topright\\, legend=c(\\M0\\, \\Mr\\, \\M1\\), col=c(\\red\\, \\blue\\, \\green\\), \n       lty=rep(1,3), cex=1, text.font=4)\n\n# print(\\histogram of M based on the G-computation\\)\nylim_CE = c( 0.0, 100)\nhist(M,xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\M: data\\)\nhist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\M[Z==0]: data\\)\nhist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\M[Z==1]: data\\)\n\n# print(\\histogram of M based on the G-computation\\)\nylim_CE = c( 0.0, 350)\nhist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\M0: G-computation\\)\nhist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\Mr: G-computation\\)\nhist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\\\,ylab=\\\\,main=\\M1: G-computation\\)\n\n# -------------------------------------------------------------------------\n# -------------------------------------------------------------------------\n# -------------------------------------------------------------------------\nrho = \\unif\\\nPOSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)\n\nNIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc\nNDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc\nATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc\n\nCE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)\nrownames(CE_tableRhoUnif) = c(\\NIE\\,\\NDE\\,\\ATE\\)\n\nNIErhoUnif = POSTresultRhoUnif$NIE\nNDErhoUnif = POSTresultRhoUnif$NDE\nATErhoUnif = POSTresultRhoUnif$ATE\n\nq95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))\nylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))\nplot(sort(NIErhoUnif),col=\\red\\,ylim=ylim_CE);par(new=T)\nplot(sort(NDErhoUnif),col=\\blue\\,ylim=ylim_CE);par(new=T)\nplot(sort(ATErhoUnif),col=\\green\\,ylim=ylim_CE)\nCE_tableRhoUnif\n\n```\n```"} -->
```r
```r
set.seed(1)
M = LITEdata$att
YY = c(Y,Y+rnorm(N,0,0.1))
MM = c(M,M)
VV = c(V,V+rnorm(N,0,0.1))
ZZ = c(Z,Z)
p_C = ncol(C)
p_C1 = sum(apply(C, 2, function(x) { all(x %in% 0:1) }))
p_C2 = p_C - p_C1
AA = rbind(C,C)
AA[(N+1):(2*N),((p_C1+1):p_C)] = AA[(N+1):(2*N),((p_C1+1):p_C)] + matrix(rnorm(p_C2*N,0,0.1),ncol=p_C2)
CC = AA
MCMCresult = EDPmediationMCMC(YY, MM, VV, ZZ, CC,
gibbs_iter, gibbs_burnin, gibbs_thin,
D, num_MC, num_MC_prior)
{
# Significance Level alpha
level = 0.05
quantile_alpha = c(level/2,1-level/2)
# the number of Gibbs Sampler stored
n_MCMC = MCMCresult$constants$n_MCMC
# Define interation check
iter_check = floor(n_MCMC/10)
M0_mc = list(NA)
Mr_mc = list(NA)
M1_mc = list(NA)
N = MCMCresult$constants$N
D = MCMCresult$constants$D
num_MC = MCMCresult$constants$num_MC
p_V = MCMCresult$constants$p_V
p_Z = MCMCresult$constants$p_Z
p_C1 = MCMCresult$constants$p_C1
p_C2 = MCMCresult$constants$p_C2
f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
a_Ysig2 = MCMCresult$priors$a_Ysig2
b_Ysig2 = MCMCresult$priors$b_Ysig2
a_Ybeta = MCMCresult$priors$a_Ybeta
B_Ybeta = MCMCresult$priors$B_Ybeta
a_Msig2 = MCMCresult$priors$a_Msig2
b_Msig2 = MCMCresult$priors$b_Msig2
a_Mbeta = MCMCresult$priors$a_Mbeta
B_Mbeta = MCMCresult$priors$B_Mbeta
a_Vsig2 = MCMCresult$priors$a_Vsig2
b_Vsig2 = MCMCresult$priors$b_Vsig2
a_Vbeta = MCMCresult$priors$a_Vbeta
B_Vbeta = MCMCresult$priors$B_Vbeta
a_pi = MCMCresult$priors$a_pi
b_pi = MCMCresult$priors$b_pi
a_mu = MCMCresult$priors$a_mu
b_mu = MCMCresult$priors$b_mu
a_tau2 = MCMCresult$priors$a_tau2
b_tau2 = MCMCresult$priors$b_tau2
alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
rho = runif(n_MCMC)
# End initial values ------------------------------------------------------------
for (post_reps in 1:n_MCMC) {
Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
rho_mc = rho[post_reps] * rep(1,D)
YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
ZpiPars_array = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
XpiPars_array = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
XmuPars_array = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
alpha_theta = alpha_theta_draws[post_reps]
alpha_omega = alpha_omega_draws[post_reps]
MCresult = EDPpostmc_concon(p_C1, p_C2,
n_k, n_rk, Ky, Kyx, max_Kx_Sy,
D, num_MC, rho_mc,
YbetaPars, Ysig2Pars,
MbetaPars, Msig2Pars,
VbetaPars_array, Vsig2Pars_array,
ZpiPars_array, XpiPars_array,
XmuPars_array, Xtau2Pars_array,
alpha_theta, alpha_omega,
f0_z0_mc, f0_z1_mc,
YbetaPrior_mc,
MbetaPrior_mc, Msig2Prior_mc,
VbetaPrior_mc, Vsig2Prior_mc,
a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
M0_mc[[post_reps]] = MCresult$M0_mc
Mr_mc[[post_reps]] = MCresult$Mr_mc
M1_mc[[post_reps]] = MCresult$M1_mc
if (post_reps %% iter_check == 0){
cat(\Post-Processing\,post_reps,\(\,(post_reps/n_MCMC)*100,\%)\,\Time:\,date(),\\n\)
}
}
distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}
M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)
mean(M)
mean(M[Z==0])
mean(M[Z==1])
# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)
# print(\dist. of M based on the data\)
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)
plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Data\,col=\green\)
legend(\topright\, legend=c(\M\, \M[Z==0]\, \M[Z==1]\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
# print(\dist. of M based on the G-computation\)
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\G-computation\,col=\green\)
abline(v = 0, col = \black\, lwd = 2)
abline(v = 1, col = \black\, lwd = 2)
legend(\topright\, legend=c(\M0\, \Mr\, \M1\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M: data\)
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==0]: data\)
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==1]: data\)
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M0: G-computation\)
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Mr: G-computation\)
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M1: G-computation\)
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = \unif\
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)
NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc
CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c(\NIE\,\NDE\,\ATE\)
NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE
q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col=\red\,ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col=\blue\,ylim=ylim_CE);par(new=T)
plot(sort(ATErhoUnif),col=\green\,ylim=ylim_CE)
CE_tableRhoUnif
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\newpage
### dist. of f(M)
<!-- rnb-text-end -->
<!-- rnb-chunk-begin -->
<!-- rnb-source-begin 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 -->
```r
```r
set.seed(1)
M = LITEdata$att
YY = c(Y,Y+rnorm(N,0,0.1),Y+rnorm(N,0,0.1),Y+rnorm(N,0,0.1))
MM = c(M,M,M,M)
VV = c(V,V+rnorm(N,0,0.1),V+rnorm(N,0,0.1),V+rnorm(N,0,0.1))
ZZ = c(Z,Z,Z,Z)
p_C = ncol(C)
p_C1 = sum(apply(C, 2, function(x) { all(x %in% 0:1) }))
p_C2 = p_C - p_C1
AA = rbind(C,C,C,C)
AA[(N+1):(4*N),((p_C1+1):p_C)] = AA[(N+1):(4*N),((p_C1+1):p_C)] + matrix(rnorm((p_C2*3*N),0,0.1),ncol=p_C2)
CC = AA
MCMCresult = EDPmediationMCMC(YY, MM, VV, ZZ, CC,
gibbs_iter, gibbs_burnin, gibbs_thin,
D, num_MC, num_MC_prior)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Bur-In End 5000 Time: Wed Feb 22 01:10:25 2023 Gibbs Iteration 250 ( 5 %) Time: Wed Feb 22 01:13:09 2023 Gibbs Iteration 500 ( 10 %) Time: Wed Feb 22 01:15:58 2023 Gibbs Iteration 750 ( 15 %) Time: Wed Feb 22 01:18:49 2023 Gibbs Iteration 1000 ( 20 %) Time: Wed Feb 22 01:21:42 2023 Gibbs Iteration 1250 ( 25 %) Time: Wed Feb 22 01:24:39 2023 Gibbs Iteration 1500 ( 30 %) Time: Wed Feb 22 01:27:45 2023 Gibbs Iteration 1750 ( 35 %) Time: Wed Feb 22 01:30:53 2023 Gibbs Iteration 2000 ( 40 %) Time: Wed Feb 22 01:34:01 2023 Gibbs Iteration 2250 ( 45 %) Time: Wed Feb 22 01:37:09 2023 Gibbs Iteration 2500 ( 50 %) Time: Wed Feb 22 01:40:16 2023 Gibbs Iteration 2750 ( 55 %) Time: Wed Feb 22 01:43:28 2023 Gibbs Iteration 3000 ( 60 %) Time: Wed Feb 22 01:46:43 2023 Gibbs Iteration 3250 ( 65 %) Time: Wed Feb 22 01:49:57 2023 Gibbs Iteration 3500 ( 70 %) Time: Wed Feb 22 01:53:13 2023 Gibbs Iteration 3750 ( 75 %) Time: Wed Feb 22 01:56:28 2023 Gibbs Iteration 4000 ( 80 %) Time: Wed Feb 22 01:59:50 2023 Gibbs Iteration 4250 ( 85 %) Time: Wed Feb 22 02:03:09 2023 Gibbs Iteration 4500 ( 90 %) Time: Wed Feb 22 02:06:24 2023 Gibbs Iteration 4750 ( 95 %) Time: Wed Feb 22 02:09:30 2023 Gibbs Iteration 5000 ( 100 %) Time: Wed Feb 22 02:12:37 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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-->
```r
```r
{
# Significance Level alpha
level = 0.05
quantile_alpha = c(level/2,1-level/2)
# the number of Gibbs Sampler stored
n_MCMC = MCMCresult$constants$n_MCMC
# Define interation check
iter_check = floor(n_MCMC/10)
M0_mc = list(NA)
Mr_mc = list(NA)
M1_mc = list(NA)
N = MCMCresult$constants$N
D = MCMCresult$constants$D
num_MC = MCMCresult$constants$num_MC
p_V = MCMCresult$constants$p_V
p_Z = MCMCresult$constants$p_Z
p_C1 = MCMCresult$constants$p_C1
p_C2 = MCMCresult$constants$p_C2
f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
a_Ysig2 = MCMCresult$priors$a_Ysig2
b_Ysig2 = MCMCresult$priors$b_Ysig2
a_Ybeta = MCMCresult$priors$a_Ybeta
B_Ybeta = MCMCresult$priors$B_Ybeta
a_Msig2 = MCMCresult$priors$a_Msig2
b_Msig2 = MCMCresult$priors$b_Msig2
a_Mbeta = MCMCresult$priors$a_Mbeta
B_Mbeta = MCMCresult$priors$B_Mbeta
a_Vsig2 = MCMCresult$priors$a_Vsig2
b_Vsig2 = MCMCresult$priors$b_Vsig2
a_Vbeta = MCMCresult$priors$a_Vbeta
B_Vbeta = MCMCresult$priors$B_Vbeta
a_pi = MCMCresult$priors$a_pi
b_pi = MCMCresult$priors$b_pi
a_mu = MCMCresult$priors$a_mu
b_mu = MCMCresult$priors$b_mu
a_tau2 = MCMCresult$priors$a_tau2
b_tau2 = MCMCresult$priors$b_tau2
alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
rho = runif(n_MCMC)
# End initial values ------------------------------------------------------------
for (post_reps in 1:n_MCMC) {
Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
rho_mc = rho[post_reps] * rep(1,D)
YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
ZpiPars_array = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
XpiPars_array = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
XmuPars_array = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
alpha_theta = alpha_theta_draws[post_reps]
alpha_omega = alpha_omega_draws[post_reps]
MCresult = EDPpostmc_concon(p_C1, p_C2,
n_k, n_rk, Ky, Kyx, max_Kx_Sy,
D, num_MC, rho_mc,
YbetaPars, Ysig2Pars,
MbetaPars, Msig2Pars,
VbetaPars_array, Vsig2Pars_array,
ZpiPars_array, XpiPars_array,
XmuPars_array, Xtau2Pars_array,
alpha_theta, alpha_omega,
f0_z0_mc, f0_z1_mc,
YbetaPrior_mc,
MbetaPrior_mc, Msig2Prior_mc,
VbetaPrior_mc, Vsig2Prior_mc,
a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
M0_mc[[post_reps]] = MCresult$M0_mc
Mr_mc[[post_reps]] = MCresult$Mr_mc
M1_mc[[post_reps]] = MCresult$M1_mc
if (post_reps %% iter_check == 0){
cat(\Post-Processing\,post_reps,\(\,(post_reps/n_MCMC)*100,\%)\,\Time:\,date(),\\n\)
}
}
distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Wed Feb 22 02:12:38 2023 Post-Processing 10 ( 20 %) Time: Wed Feb 22 02:12:39 2023 Post-Processing 15 ( 30 %) Time: Wed Feb 22 02:12:39 2023 Post-Processing 20 ( 40 %) Time: Wed Feb 22 02:12:40 2023 Post-Processing 25 ( 50 %) Time: Wed Feb 22 02:12:41 2023 Post-Processing 30 ( 60 %) Time: Wed Feb 22 02:12:42 2023 Post-Processing 35 ( 70 %) Time: Wed Feb 22 02:12:42 2023 Post-Processing 40 ( 80 %) Time: Wed Feb 22 02:12:43 2023 Post-Processing 45 ( 90 %) Time: Wed Feb 22 02:12:44 2023 Post-Processing 50 ( 100 %) Time: Wed Feb 22 02:12:45 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTTBfbWMgPSB1bmxpc3QoZGlzdE0kTTBfbWMpXG5Ncl9tYyA9IHVubGlzdChkaXN0TSRNcl9tYylcbk0xX21jID0gdW5saXN0KGRpc3RNJE0xX21jKVxuXG5tZWFuKE0pXG5gYGBcbmBgYCJ9 -->
```r
```r
M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)
mean(M)
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuNTMwOTNcbiJ9 -->
[1] 0.53093
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTBdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==0])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuNTI0MDUzNlxuIn0= -->
[1] 0.5240536
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxubWVhbihNW1o9PTFdKVxuYGBgXG5gYGAifQ== -->
```r
```r
mean(M[Z==1])
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiWzFdIDAuNTM4MzE5MlxuIn0= -->
[1] 0.5383192
<!-- rnb-output-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuIyBuID0gTUNNQ3Jlc3VsdCRjb25zdGFudHMkRFxubiA9IDFlNVxueWxpbV9DRSA9IGMoIDAuMCwgMi4wKVxueGxpbV9DRSA9IGMobWluKE0pLTEsIG1heChNKSsxKVxuXG4jIHByaW50KFxcZGlzdC4gb2YgTSBiYXNlZCBvbiB0aGUgZGF0YVxcKVxucGxvdChkZW5zaXR5KE0sbj1uKSx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXFxcLGNvbD1cXHJlZFxcKTtwYXIobmV3PVQpXG5wbG90KGRlbnNpdHkoTVtaPT0wXSxuPW4pLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcXFwsY29sPVxcYmx1ZVxcKTtwYXIobmV3PVQpXG5gYGBcbmBgYHJcbnBsb3QoZGVuc2l0eShNW1o9PTFdLG49bikseGxpbT14bGltX0NFLHlsaW09eWxpbV9DRSx4bGFiPVxcXFwseWxhYj1cXFxcLG1haW49XFxEYXRhXFwsY29sPVxcZ3JlZW5cXClcbmxlZ2VuZChcXHRvcHJpZ2h0XFwsIGxlZ2VuZD1jKFxcTVxcLCBcXE1bWj09MF1cXCwgXFxNW1o9PTFdXFwpLCBjb2w9YyhcXHJlZFxcLCBcXGJsdWVcXCwgXFxncmVlblxcKSwgXG4gICAgICAgbHR5PXJlcCgxLDMpLCBjZXg9MSwgdGV4dC5mb250PTQpXG5gYGBcbmBgYCJ9 -->
```r
```r
# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)
# print(\dist. of M based on the data\)
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Data\,col=\green\)
legend(\topright\, legend=c(\M\, \M[Z==0]\, \M[Z==1]\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img src="data:image/png;base64,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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin 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 -->
```r
```r
# print(\dist. of M based on the G-computation\)
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\red\);par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\\,col=\blue\);par(new=T)plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\G-computation\,col=\green\)
abline(v = 0, col = \black\, lwd = 2)abline(v = 1, col = \black\, lwd = 2)
legend(\topright\, legend=c(\M0\, \Mr\, \M1\), col=c(\red\, \blue\, \green\),
lty=rep(1,3), cex=1, text.font=4)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDEwMClcbmhpc3QoTSx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE06IGRhdGFcXClcbmBgYFxuYGBgIn0= -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTBdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0wXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==0]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNW1o9PTFdLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTVtaPT0xXTogZGF0YVxcKVxuYGBgXG5gYGAifQ== -->
```r
```r
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M[Z==1]: data\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIHByaW50KFxcaGlzdG9ncmFtIG9mIE0gYmFzZWQgb24gdGhlIEctY29tcHV0YXRpb25cXClcbnlsaW1fQ0UgPSBjKCAwLjAsIDM1MClcbmhpc3QoTTBfbWNbd2hpY2goKE0wX21jPnhsaW1fQ0VbMV0pKihNMF9tYzx4bGltX0NFWzJdKT09MSldLDFlMyx4bGltPXhsaW1fQ0UseWxpbT15bGltX0NFLHhsYWI9XFxcXCx5bGFiPVxcXFwsbWFpbj1cXE0wOiBHLWNvbXB1dGF0aW9uXFwpXG5gYGBcbmBgYCJ9 -->
```r
```r
# print(\histogram of M based on the G-computation\)
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M0: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNcl9tY1t3aGljaCgoTXJfbWM+eGxpbV9DRVsxXSkqKE1yX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTXI6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\Mr: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuaGlzdChNMV9tY1t3aGljaCgoTTFfbWM+eGxpbV9DRVsxXSkqKE0xX21jPHhsaW1fQ0VbMl0pPT0xKV0sMWUzLHhsaW09eGxpbV9DRSx5bGltPXlsaW1fQ0UseGxhYj1cXFxcLHlsYWI9XFxcXCxtYWluPVxcTTE6IEctY29tcHV0YXRpb25cXClcbmBgYFxuYGBgIn0= -->
```r
```r
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab=\\,ylab=\\,main=\M1: G-computation\)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
<img 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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG4jIC0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS1cbiMgLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLVxuIyAtLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tLS0tXG5yaG8gPSBcXHVuaWZcXFxuUE9TVHJlc3VsdFJob1VuaWYgPSBFRFBtZWRpYXRpb25QT1NUKE1DTUNyZXN1bHQsIGVzdHR5cGUsIHJobywgc2F2ZV9jbHVzdGVyKVxuYGBgXG5gYGAifQ== -->
```r
```r
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = \unif\
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)
<!-- rnb-source-end -->
<!-- rnb-output-begin 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 -->
Post-Processing 5 ( 10 %) Time: Wed Feb 22 02:12:50 2023 Post-Processing 10 ( 20 %) Time: Wed Feb 22 02:12:50 2023 Post-Processing 15 ( 30 %) Time: Wed Feb 22 02:12:51 2023 Post-Processing 20 ( 40 %) Time: Wed Feb 22 02:12:52 2023 Post-Processing 25 ( 50 %) Time: Wed Feb 22 02:12:53 2023 Post-Processing 30 ( 60 %) Time: Wed Feb 22 02:12:53 2023 Post-Processing 35 ( 70 %) Time: Wed Feb 22 02:12:54 2023 Post-Processing 40 ( 80 %) Time: Wed Feb 22 02:12:55 2023 Post-Processing 45 ( 90 %) Time: Wed Feb 22 02:12:56 2023 Post-Processing 50 ( 100 %) Time: Wed Feb 22 02:12:56 2023
<!-- rnb-output-end -->
<!-- rnb-source-begin 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 -->
```r
```r
NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc
CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c(\NIE\,\NDE\,\ATE\)
NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE
q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col=\red\,ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col=\blue\,ylim=ylim_CE);par(new=T)plot(sort(ATErhoUnif),col=\green\,ylim=ylim_CE)
<!-- rnb-source-end -->
<!-- rnb-plot-begin -->
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" />
<!-- rnb-plot-end -->
<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuQ0VfdGFibGVSaG9VbmlmXG5gYGBcbmBgYCJ9 -->
```r
```r
CE_tableRhoUnif
<!-- rnb-source-end -->
<!-- rnb-output-begin eyJkYXRhIjoiICAgICAgIGVzdGltYXRlcyAgICAgICAgc2QgcXVhbnRpbGUwMjUgcXVhbnRpbGU5NzUgQ0lsZW5ndGg5NVxuTklFICAwLjAwNTQ1NDY5NCAwLjE1NTQ5ODYgIC0wLjI0ODQ1NjggICAwLjM4ODU3ODkgIDAuNjM3MDM1N1xuTkRFIC0zLjI4NjY0NzM0OCAwLjM3MTgxNDkgIC00LjEyNjI4MzYgIC0yLjYyMTU3MTQgIDEuNTA0NzEyM1xuQVRFIC0zLjI4MTE5MjY1NCAwLjQwNjQ2NTUgIC00LjEzNzc0MzYgIC0yLjcyNDczNzkgIDEuNDEzMDA1OFxuIn0= -->
estimates sd quantile025 quantile975 CIlength95NIE 0.005454694 0.1554986 -0.2484568 0.3885789 0.6370357 NDE -3.286647348 0.3718149 -4.1262836 -2.6215714 1.5047123 ATE -3.281192654 0.4064655 -4.1377436 -2.7247379 1.4130058 ```
---
title: "Rural LITE data: f(M)"
output:
  html_notebook: default
---

# DATA 
```{r}
# Load R packages
library(Rcpp)
library(RcppArmadillo)
library(dplyr)
library(mgcv)
library(openxlsx) 
library(lme4) 

# Set Directory
setwd("C:/Users/WooJung/Documents/Rproject/EDPmediationpost/RealDataAnalysis")
# setwd("C:/Users/Jennifer/Desktop/EDPmediation/RealDataAnalysis")

# -------------------------------------------------------------------------
# ---------------------------------- DATA ---------------------------------
# -------------------------------------------------------------------------
# Here are the details for this analysis:
# - outcome: 24 month weight change (spreadsheet 2)
# - mediator - Phase 2 attendance (measured as a percentage) - spreadsheet 1
# - baseline confounders - mostly Table 1 from the paper and previous spreadsheet I sent
# - potential post treatment confounder - 6 month weight (or 6 month weight change) - spreadsheet 4
# - ok to merge control/low and moderate/high arms (so only two arms)

# Load Data
data1 = read.xlsx('RL_WTS_24mo_MD.xlsx', sheet = 'wts24', startRow = 2)
# data1$ID
# data1$CONDITION
# data1$TRTARM
# data1$WTKG_24

# no edu+income data here
data2 = read.xlsx('final_baseline_data_RL.xlsx')
# data2$ID
# data2$CONDITION
# data2$TRTARM
# data2$sex
# data2$race
# data2$AGE_WK1
# data2$HTSV1
# data2$WTKG_SV2
# data2$BMI_SV2

data3 = read.xlsx('tx data att - 082413 - all summary vars.xlsx')
# data3$ID
# data3$CONDITION
# data3$TRTARM
# data3$p2_attmu_tot_pc

# 
data4 = read.xlsx('RLITE_LABS_WTS.xlsx', sheet = 'WTS_0')
# data4$ID
# data4$CONDITION
# data4$TRTARM
# data4$WTKG_0

# 
data5 = read.xlsx('RLITE_LABS_WTS.xlsx', sheet = 'WTS_6')
# data5$ID
# data5$CONDITION
# data5$TRTARM
# data5$WTKG_6

# 
data6 = read.xlsx('RLITE_LABS_WTS.xlsx', sheet = 'WTS_24')
# data6$ID
# data6$CONDITION
# data6$TRTARM
# data6$WTKG_24

# - mediator - Phase 2 attendance (measured as a percentage) - spreadsheet 1
# - baseline confounders - mostly Table 1 from the paper and previous spreadsheet I sent
sum(abs(data2$ID!=data3$ID))
sum(abs(data2$ID!=data4$ID))
sum(abs(data2$ID!=data5$ID))
sum(abs(data2$ID!=data6$ID))

# we may add education and income 
# Just ignore the warning message! 
LITEdata = data.frame(id = data6$ID, 
                      cond = data6$CONDITION,
                      trt = as.numeric(data6$TRTARM),
                      wgt24 = as.numeric(data6$WTKG_24), 
                      wgt6 = as.numeric(data5$WTKG_6), 
                      wgt0 = as.numeric(data4$WTKG_0),
                      att = as.numeric(data3$p2_attmu_tot_pc), 
                      sex = as.numeric(data2$sex), 
                      race = ifelse(as.numeric(data2$nih_race_BIQ)==5,1,0), # white no not
                      age = as.numeric(data2$AGE_WK1), 
                      bmi = as.numeric(data2$BMI_SV2))

# Drop variables with NAs
N = nrow(LITEdata)
sum(is.na(LITEdata$cond))
sum(is.na(LITEdata$att))
sum(is.na(LITEdata$sex))
sum(is.na(LITEdata$age))
sum(is.na(LITEdata$race))
sum(is.na(LITEdata$bmi))
sum(is.na(LITEdata$wgt0))
sum(is.na(LITEdata$wgt6))
sum(is.na(LITEdata$wgt24))

# wgt6: 56 NAs (among N = 612)
sum(is.na(LITEdata$wgt6))
# wgt24: 121 NAs (among N = 612)
sum(is.na(LITEdata$wgt24))
# both NA: 37 NAs (among N = 612)
sum(is.na(LITEdata$wgt6)*is.na(LITEdata$wgt24))
# Total NA: 140 NAs (among N = 612)
sum((is.na(LITEdata$wgt6) + is.na(LITEdata$wgt24))>=1)

# Delete NAs -> No!
# LITEdata = LITEdata[-which(apply(is.na(LITEdata), 1, sum)>0),]

# Outcome: Weight change between wgt 0 and wgt 24
LITEdata$wgtchange0_24 = LITEdata$wgt24 - LITEdata$wgt0
# Post-treatment confounder: Weight change between wgt 0 and wgt 6
LITEdata$wgtchange0_6 = LITEdata$wgt6 - LITEdata$wgt0
# Post-treatment confounder: Weight change between wgt 0 and wgt 6
LITEdata$trtmerge = ifelse(LITEdata$trt<2.5,0,1)

{
  esttype = "mean"
  # esttype = "median"
  save_cluster = TRUE
  # save_cluster = FALSE
  
  # Extract ID for simulated dataset (specific to LSF computing cluster)
  # Note: The LSB_JOBINDEX is specified in the bsub command using the -J
  # option
  run_ID = 1
  
  # Specify the seed so can repeat simulation later if necessary
  set.seed(run_ID)
  
  # ------------------------------------------------------------------------------
  # Define of constants (adjust to fit the data generating scenario) -------------
  # ------------------------------------------------------------------------------
  # Define number of observations per draw when using Monte Carlo integration to
  # integrate out confounders
  D = 1e4
  
  # Define number of Markov Chain Monte Carlo (MCMC) draws in Gibbs Sampler
  # Define number of MCMC draws to 'burn' in Gibbs Sampler (check convergence)
  # gibbs_iter = 1e5
  # gibbs_burnin = 5e4
  gibbs_iter = 5e3
  gibbs_burnin = 5e3
  
  # the number of MC integration per iteration for a MCMC chain
  # gibbs_thin = 10
  gibbs_thin = 100
  # gibbs_num = 2e3
  # gibbs_thin = floor(gibbs_iter/gibbs_num)
  
  # Define number of Monte Carlo draws when using Monte Carlo integration to
  # integrate out confounders
  # num_MC = 1e4
  # num_MC = 1e3
  num_MC = 1e2
  
  # num_MC_prior
  num_MC_prior = 1e5
  
  rho = "unif"
  
  # ------------------------------------------------------------------------------
  # End Definition of Constants --------------------------------------------------
  # ------------------------------------------------------------------------------
}
```

### EDPM
```{r}
# -------------------------------------------------------------------------
# ------------------ EDP with a post-treatment confounder -----------------
# -------------------------------------------------------------------------
setwd("C:/Users/WooJung/Documents/Rproject/EDPmediationpost/RealDataAnalysis")

# EDPM
Y = LITEdata$wgt24
M = LITEdata$att
V = LITEdata$wgt6
Z = LITEdata$trtmerge
C = cbind(LITEdata$sex,
          LITEdata$race,
          LITEdata$age,
          LITEdata$bmi,
          LITEdata$wgt0)
```

\newpage
### dist. of (Y,M)
```{r}
set.seed(1)
M = LITEdata$att

library(MASS)
library(plotly)
ind_naY = which(is.na(Y))
x = M[-ind_naY]
y = Y[-ind_naY]
den3d = kde2d(x, y, n = 200)

plot_ly(x=den3d$x, y=den3d$y, z=t(den3d$z)) %>% add_surface()

plot(density(x))
plot(density(y))
```



\newpage
### EDPM (Y, M , Z, C)
```{r}
# -------------------------------------------------------------------------
# ------------------ EDP with a post-treatment confounder -----------------
# -------------------------------------------------------------------------
setwd("C:/Users/WooJung/Documents/Rproject/EDPmediationpost/RealDataAnalysis")
sourceCpp("EDPsource_cpp_realdata.cpp")
source("EDPsource_r_realdata.R")

{
  # EDPM
  Y = LITEdata$wgt24
  M = LITEdata$att
  V = LITEdata$wgt6
  Z = LITEdata$trtmerge
  C = cbind(LITEdata$sex,
            LITEdata$race,
            LITEdata$age,
            LITEdata$bmi,
            LITEdata$wgt0)
  
  MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
                                gibbs_iter, gibbs_burnin, gibbs_thin,
                                D, num_MC, num_MC_prior)
  {
    # Significance Level alpha
    level = 0.05
    quantile_alpha = c(level/2,1-level/2)
  
    # the number of Gibbs Sampler stored
    n_MCMC = MCMCresult$constants$n_MCMC
  
    # Define interation check
    iter_check = floor(n_MCMC/10)
  
    M0_mc = list(NA)
    Mr_mc = list(NA)
    M1_mc = list(NA)
  
    N = MCMCresult$constants$N
    D = MCMCresult$constants$D
    num_MC = MCMCresult$constants$num_MC
    p_V = MCMCresult$constants$p_V
    p_Z = MCMCresult$constants$p_Z
    p_C1 = MCMCresult$constants$p_C1
    p_C2 = MCMCresult$constants$p_C2
  
    f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
    f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
    YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
    MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
    Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
    VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
    Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
  
    a_Ysig2 = MCMCresult$priors$a_Ysig2
    b_Ysig2 = MCMCresult$priors$b_Ysig2
    a_Ybeta = MCMCresult$priors$a_Ybeta
    B_Ybeta = MCMCresult$priors$B_Ybeta
    a_Msig2 = MCMCresult$priors$a_Msig2
    b_Msig2 = MCMCresult$priors$b_Msig2
    a_Mbeta = MCMCresult$priors$a_Mbeta
    B_Mbeta = MCMCresult$priors$B_Mbeta
    a_Vsig2 = MCMCresult$priors$a_Vsig2
    b_Vsig2 = MCMCresult$priors$b_Vsig2
    a_Vbeta = MCMCresult$priors$a_Vbeta
    B_Vbeta = MCMCresult$priors$B_Vbeta
    a_pi   = MCMCresult$priors$a_pi
    b_pi   = MCMCresult$priors$b_pi
    a_mu   = MCMCresult$priors$a_mu
    b_mu   = MCMCresult$priors$b_mu
    a_tau2 = MCMCresult$priors$a_tau2
    b_tau2 = MCMCresult$priors$b_tau2
  
    alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
    alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
  
    rho = runif(n_MCMC)
  
    # End initial values ------------------------------------------------------------
    for (post_reps in 1:n_MCMC) {
      Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
      Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
      n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
      n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
      max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
  
      rho_mc = rho[post_reps] * rep(1,D)
      YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
      Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
      MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
      Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
      VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
      Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
      ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
      XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
      XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
      Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
      alpha_theta = alpha_theta_draws[post_reps]
      alpha_omega = alpha_omega_draws[post_reps]
  
      MCresult = EDPpostmc_concon(p_C1, p_C2,
                                  n_k, n_rk, Ky, Kyx, max_Kx_Sy,
                                  D, num_MC, rho_mc,
                                  YbetaPars, Ysig2Pars,
                                  MbetaPars, Msig2Pars,
                                  VbetaPars_array, Vsig2Pars_array,
                                  ZpiPars_array, XpiPars_array,
                                  XmuPars_array, Xtau2Pars_array,
                                  alpha_theta, alpha_omega,
                                  f0_z0_mc, f0_z1_mc,
                                  YbetaPrior_mc,
                                  MbetaPrior_mc, Msig2Prior_mc,
                                  VbetaPrior_mc, Vsig2Prior_mc,
                                  a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                  a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                  a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                  a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
  
      M0_mc[[post_reps]] = MCresult$M0_mc
      Mr_mc[[post_reps]] = MCresult$Mr_mc
      M1_mc[[post_reps]] = MCresult$M1_mc
  
      if (post_reps %% iter_check == 0){
        cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
      }
    }
  
    distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
  }
  
  M0_mc = unlist(distM$M0_mc)
  Mr_mc = unlist(distM$Mr_mc)
  M1_mc = unlist(distM$M1_mc)
  
  mean(M)
  mean(M[Z==0])
  mean(M[Z==1])
  
  # n = MCMCresult$constants$D
  n = 1e4
  ylim_CE = c( 0.0, 2.0)
  xlim_CE = c( min(M) - 1, max(M)+1)
  
  # print("dist. of M based on the data")
  plot(density(M),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
  plot(density(M[Z==0]),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
  plot(density(M[Z==1]),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
  legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
         lty=rep(1,3), cex=1, text.font=4)
  
  # print("dist. of M based on the G-computation")
  ylim_CE = c( 0.0, 2.0)
  plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)]),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
  plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)]),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
  plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)]),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
  # abline(v = 0, col = "black", lwd = 2)
  # abline(v = 1, col = "black", lwd = 2)
  legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
         lty=rep(1,3), cex=1, text.font=4)
  
  # print("histogram of M based on the G-computation")
  ylim_CE = c( 0.0, 80)
  hist(M,20,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
  hist(M[Z==0],20,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
  hist(M[Z==1],20,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")
  
  # print("histogram of M based on the G-computation")
  ylim_CE = c( 0.0, 8000)
  hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
  hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
  hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")
  
  # Define design matrix
  p_C = ncol(C)
  p_C1 = sum(apply(C, 2, function(x) { all(x %in% 0:1) }))
  p_C2 = p_C - p_C1
  if (p_C1>0 && p_C2>0){
    C1 = C[,1:p_C1]
    C2 = C[,(p_C1+1):(p_C1+p_C2)]
    scaC2 = apply(C2, 2, scale)
    scaC = cbind(C1, scaC2)
  } else if (p_C2>0){
    scaC = apply(C, 2, scale)
  } else {
    scaC = C
  }
  X = cbind(Z, scaC)
  matX = cbind(1, X)
  matV = cbind(1, Z, V, scaC)
}
apply(matV[-which(is.na(V)),] %*% MCMCresult$MCMCposteriors$MbetaLists[[post_reps]], 2, mean)
apply(matV[-which(is.na(V)),] %*% MCMCresult$MCMCposteriors$MbetaLists[[post_reps]], 2, median)
n_rk
# MCMCresult$MCMCposteriors$n_rk
```

\newpage
### EDPM (Y, M , Z, C)
```{r}
# -------------------------------------------------------------------------
# ------------------ EDP with a post-treatment confounder -----------------
# -------------------------------------------------------------------------
setwd("C:/Users/WooJung/Documents/Rproject/EDPmediationpost/RealDataAnalysis")
sourceCpp("EDPsource_cpp_realdata.cpp")
source("EDPsource_r_realdata.R")

# EDPM
Y = LITEdata$wgt24
M = LITEdata$att
V = LITEdata$wgt6
Z = LITEdata$trtmerge
C = cbind(LITEdata$sex,
          LITEdata$race,
          LITEdata$age,
          LITEdata$bmi,
          LITEdata$wgt0)

eps = - 0.1
newM = M * (1 + 2 * eps) / 2 + 0.5
newM = log(newM/(1-newM))

# a = (((invlogit(newM) - 0.5) * 2 / (1 + 2 * eps))^{3})/2 + 0.5
# a - M

hist(M)
plot(density(M))
hist(newM)
plot(density(newM))

M = newM

MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
                              gibbs_iter, gibbs_burnin, gibbs_thin,
                              D, num_MC, num_MC_prior)
{
  # Significance Level alpha
  level = 0.05
  quantile_alpha = c(level/2,1-level/2)

  # the number of Gibbs Sampler stored
  n_MCMC = MCMCresult$constants$n_MCMC

  # Define interation check
  iter_check = floor(n_MCMC/10)

  M0_mc = list(NA)
  Mr_mc = list(NA)
  M1_mc = list(NA)

  N = MCMCresult$constants$N
  D = MCMCresult$constants$D
  num_MC = MCMCresult$constants$num_MC
  p_V = MCMCresult$constants$p_V
  p_Z = MCMCresult$constants$p_Z
  p_C1 = MCMCresult$constants$p_C1
  p_C2 = MCMCresult$constants$p_C2

  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc

  a_Ysig2 = MCMCresult$priors$a_Ysig2
  b_Ysig2 = MCMCresult$priors$b_Ysig2
  a_Ybeta = MCMCresult$priors$a_Ybeta
  B_Ybeta = MCMCresult$priors$B_Ybeta
  a_Msig2 = MCMCresult$priors$a_Msig2
  b_Msig2 = MCMCresult$priors$b_Msig2
  a_Mbeta = MCMCresult$priors$a_Mbeta
  B_Mbeta = MCMCresult$priors$B_Mbeta
  a_Vsig2 = MCMCresult$priors$a_Vsig2
  b_Vsig2 = MCMCresult$priors$b_Vsig2
  a_Vbeta = MCMCresult$priors$a_Vbeta
  B_Vbeta = MCMCresult$priors$B_Vbeta
  a_pi   = MCMCresult$priors$a_pi
  b_pi   = MCMCresult$priors$b_pi
  a_mu   = MCMCresult$priors$a_mu
  b_mu   = MCMCresult$priors$b_mu
  a_tau2 = MCMCresult$priors$a_tau2
  b_tau2 = MCMCresult$priors$b_tau2

  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws

  rho = runif(n_MCMC)

  # End initial values ------------------------------------------------------------
  for (post_reps in 1:n_MCMC) {
    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]

    rho_mc = rho[post_reps] * rep(1,D)
    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
    alpha_theta = alpha_theta_draws[post_reps]
    alpha_omega = alpha_omega_draws[post_reps]

    MCresult = EDPpostmc_concon(p_C1, p_C2,
                                n_k, n_rk, Ky, Kyx, max_Kx_Sy,
                                D, num_MC, rho_mc,
                                YbetaPars, Ysig2Pars,
                                MbetaPars, Msig2Pars,
                                VbetaPars_array, Vsig2Pars_array,
                                ZpiPars_array, XpiPars_array,
                                XmuPars_array, Xtau2Pars_array,
                                alpha_theta, alpha_omega,
                                f0_z0_mc, f0_z1_mc,
                                YbetaPrior_mc,
                                MbetaPrior_mc, Msig2Prior_mc,
                                VbetaPrior_mc, Vsig2Prior_mc,
                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)

    M0_mc[[post_reps]] = MCresult$M0_mc
    Mr_mc[[post_reps]] = MCresult$Mr_mc
    M1_mc[[post_reps]] = MCresult$M1_mc

    if (post_reps %% iter_check == 0){
      cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
    }
  }

  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}

M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)

mean(M)
mean(M[Z==0])
mean(M[Z==1])

# n = MCMCresult$constants$D
n = 1e4
ylim_CE = c( 0.0, 2.0)
xlim_CE = c( min(M) - 1, max(M)+1)

# print("dist. of M based on the data")
plot(density(M),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(M[Z==0]),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M[Z==1]),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("dist. of M based on the G-computation")
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)]),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)]),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)]),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
# abline(v = 0, col = "black", lwd = 2)
# abline(v = 1, col = "black", lwd = 2)
legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 50)
hist(M,20,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
hist(M[Z==0],20,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
hist(M[Z==1],20,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")

# Define design matrix
p_C = ncol(C)
p_C1 = sum(apply(C, 2, function(x) { all(x %in% 0:1) }))
p_C2 = p_C - p_C1
if (p_C1>0 && p_C2>0){
  C1 = C[,1:p_C1]
  C2 = C[,(p_C1+1):(p_C1+p_C2)]
  scaC2 = apply(C2, 2, scale)
  scaC = cbind(C1, scaC2)
} else if (p_C2>0){
  scaC = apply(C, 2, scale)
} else {
  scaC = C
}
X = cbind(Z, scaC)
matX = cbind(1, X)
matV = cbind(1, Z, V, scaC)
apply(matV[-which(is.na(V)),] %*% MCMCresult$MCMCposteriors$MbetaLists[[post_reps]], 2, mean)
apply(matV[-which(is.na(V)),] %*% MCMCresult$MCMCposteriors$MbetaLists[[post_reps]], 2, median)
n_rk
```













\newpage
### dist. of f(M) = M
```{r}
set.seed(1)
M = LITEdata$att

MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
                              gibbs_iter, gibbs_burnin, gibbs_thin,
                              D, num_MC, num_MC_prior)

{
  # Significance Level alpha
  level = 0.05
  quantile_alpha = c(level/2,1-level/2)
  
  # the number of Gibbs Sampler stored
  n_MCMC = MCMCresult$constants$n_MCMC
  
  # Define interation check
  iter_check = floor(n_MCMC/10)
  
  M0_mc = list(NA)
  Mr_mc = list(NA)
  M1_mc = list(NA)
  
  N = MCMCresult$constants$N
  D = MCMCresult$constants$D
  num_MC = MCMCresult$constants$num_MC
  p_V = MCMCresult$constants$p_V
  p_Z = MCMCresult$constants$p_Z
  p_C1 = MCMCresult$constants$p_C1
  p_C2 = MCMCresult$constants$p_C2
  
  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
  
  a_Ysig2 = MCMCresult$priors$a_Ysig2
  b_Ysig2 = MCMCresult$priors$b_Ysig2
  a_Ybeta = MCMCresult$priors$a_Ybeta
  B_Ybeta = MCMCresult$priors$B_Ybeta
  a_Msig2 = MCMCresult$priors$a_Msig2
  b_Msig2 = MCMCresult$priors$b_Msig2
  a_Mbeta = MCMCresult$priors$a_Mbeta
  B_Mbeta = MCMCresult$priors$B_Mbeta
  a_Vsig2 = MCMCresult$priors$a_Vsig2
  b_Vsig2 = MCMCresult$priors$b_Vsig2
  a_Vbeta = MCMCresult$priors$a_Vbeta
  B_Vbeta = MCMCresult$priors$B_Vbeta
  a_pi   = MCMCresult$priors$a_pi
  b_pi   = MCMCresult$priors$b_pi
  a_mu   = MCMCresult$priors$a_mu
  b_mu   = MCMCresult$priors$b_mu
  a_tau2 = MCMCresult$priors$a_tau2
  b_tau2 = MCMCresult$priors$b_tau2
  
  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
  
  rho = runif(n_MCMC)
  
  # End initial values ------------------------------------------------------------
  for (post_reps in 1:n_MCMC) {
    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
    
    rho_mc = rho[post_reps] * rep(1,D)
    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
    alpha_theta = alpha_theta_draws[post_reps]
    alpha_omega = alpha_omega_draws[post_reps]
    
    MCresult = EDPpostmc_concon(p_C1, p_C2,
                                n_k, n_rk, Ky, Kyx, max_Kx_Sy, 
                                D, num_MC, rho_mc,
                                YbetaPars, Ysig2Pars,
                                MbetaPars, Msig2Pars,
                                VbetaPars_array, Vsig2Pars_array,
                                ZpiPars_array, XpiPars_array, 
                                XmuPars_array, Xtau2Pars_array,
                                alpha_theta, alpha_omega, 
                                f0_z0_mc, f0_z1_mc,
                                YbetaPrior_mc, 
                                MbetaPrior_mc, Msig2Prior_mc,
                                VbetaPrior_mc, Vsig2Prior_mc,
                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
    
    M0_mc[[post_reps]] = MCresult$M0_mc
    Mr_mc[[post_reps]] = MCresult$Mr_mc
    M1_mc[[post_reps]] = MCresult$M1_mc
    
    if (post_reps %% iter_check == 0){
      cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
    }
  }
  
  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}

M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)

mean(M)
mean(M[Z==0])
mean(M[Z==1])

# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)

# print("dist. of M based on the data")
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("dist. of M based on the G-computation")
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
abline(v = 0, col = "black", lwd = 2)
abline(v = 1, col = "black", lwd = 2)
legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")

# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = "unif"
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)

NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc

CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c("NIE","NDE","ATE")

NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE

q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col="red",ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col="blue",ylim=ylim_CE);par(new=T)
plot(sort(ATErhoUnif),col="green",ylim=ylim_CE)
CE_tableRhoUnif

```

\newpage
### dist. of f(M) = scale(M)
```{r}
set.seed(1)
M = LITEdata$att
M = as.numeric(scale(M))

MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
                              gibbs_iter, gibbs_burnin, gibbs_thin,
                              D, num_MC, num_MC_prior)

{
  # Significance Level alpha
  level = 0.05
  quantile_alpha = c(level/2,1-level/2)
  
  # the number of Gibbs Sampler stored
  n_MCMC = MCMCresult$constants$n_MCMC
  
  # Define interation check
  iter_check = floor(n_MCMC/10)
  
  M0_mc = list(NA)
  Mr_mc = list(NA)
  M1_mc = list(NA)
  
  N = MCMCresult$constants$N
  D = MCMCresult$constants$D
  num_MC = MCMCresult$constants$num_MC
  p_V = MCMCresult$constants$p_V
  p_Z = MCMCresult$constants$p_Z
  p_C1 = MCMCresult$constants$p_C1
  p_C2 = MCMCresult$constants$p_C2
  
  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
  
  a_Ysig2 = MCMCresult$priors$a_Ysig2
  b_Ysig2 = MCMCresult$priors$b_Ysig2
  a_Ybeta = MCMCresult$priors$a_Ybeta
  B_Ybeta = MCMCresult$priors$B_Ybeta
  a_Msig2 = MCMCresult$priors$a_Msig2
  b_Msig2 = MCMCresult$priors$b_Msig2
  a_Mbeta = MCMCresult$priors$a_Mbeta
  B_Mbeta = MCMCresult$priors$B_Mbeta
  a_Vsig2 = MCMCresult$priors$a_Vsig2
  b_Vsig2 = MCMCresult$priors$b_Vsig2
  a_Vbeta = MCMCresult$priors$a_Vbeta
  B_Vbeta = MCMCresult$priors$B_Vbeta
  a_pi   = MCMCresult$priors$a_pi
  b_pi   = MCMCresult$priors$b_pi
  a_mu   = MCMCresult$priors$a_mu
  b_mu   = MCMCresult$priors$b_mu
  a_tau2 = MCMCresult$priors$a_tau2
  b_tau2 = MCMCresult$priors$b_tau2
  
  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
  
  rho = runif(n_MCMC)
  
  # End initial values ------------------------------------------------------------
  for (post_reps in 1:n_MCMC) {
    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
    
    rho_mc = rho[post_reps] * rep(1,D)
    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
    alpha_theta = alpha_theta_draws[post_reps]
    alpha_omega = alpha_omega_draws[post_reps]
    
    MCresult = EDPpostmc_concon(p_C1, p_C2,
                                n_k, n_rk, Ky, Kyx, max_Kx_Sy, 
                                D, num_MC, rho_mc,
                                YbetaPars, Ysig2Pars,
                                MbetaPars, Msig2Pars,
                                VbetaPars_array, Vsig2Pars_array,
                                ZpiPars_array, XpiPars_array, 
                                XmuPars_array, Xtau2Pars_array,
                                alpha_theta, alpha_omega, 
                                f0_z0_mc, f0_z1_mc,
                                YbetaPrior_mc, 
                                MbetaPrior_mc, Msig2Prior_mc,
                                VbetaPrior_mc, Vsig2Prior_mc,
                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
    
    M0_mc[[post_reps]] = MCresult$M0_mc
    Mr_mc[[post_reps]] = MCresult$Mr_mc
    M1_mc[[post_reps]] = MCresult$M1_mc
    
    if (post_reps %% iter_check == 0){
      cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
    }
  }
  
  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}

M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)

mean(M)
mean(M[Z==0])
mean(M[Z==1])

# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)

# print("dist. of M based on the data")
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("dist. of M based on the G-computation")
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
abline(v = 0, col = "black", lwd = 2)
abline(v = 1, col = "black", lwd = 2)
legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")

# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = "unif"
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)

NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc

CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c("NIE","NDE","ATE")

NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE

q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col="red",ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col="blue",ylim=ylim_CE);par(new=T)
plot(sort(ATErhoUnif),col="green",ylim=ylim_CE)
CE_tableRhoUnif

```

\newpage
### dist. of f(M) = exp(M)
```{r}
set.seed(1)
M = LITEdata$att
M = exp(M)

MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
                              gibbs_iter, gibbs_burnin, gibbs_thin,
                              D, num_MC, num_MC_prior)

{
  # Significance Level alpha
  level = 0.05
  quantile_alpha = c(level/2,1-level/2)
  
  # the number of Gibbs Sampler stored
  n_MCMC = MCMCresult$constants$n_MCMC
  
  # Define interation check
  iter_check = floor(n_MCMC/10)
  
  M0_mc = list(NA)
  Mr_mc = list(NA)
  M1_mc = list(NA)
  
  N = MCMCresult$constants$N
  D = MCMCresult$constants$D
  num_MC = MCMCresult$constants$num_MC
  p_V = MCMCresult$constants$p_V
  p_Z = MCMCresult$constants$p_Z
  p_C1 = MCMCresult$constants$p_C1
  p_C2 = MCMCresult$constants$p_C2
  
  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
  
  a_Ysig2 = MCMCresult$priors$a_Ysig2
  b_Ysig2 = MCMCresult$priors$b_Ysig2
  a_Ybeta = MCMCresult$priors$a_Ybeta
  B_Ybeta = MCMCresult$priors$B_Ybeta
  a_Msig2 = MCMCresult$priors$a_Msig2
  b_Msig2 = MCMCresult$priors$b_Msig2
  a_Mbeta = MCMCresult$priors$a_Mbeta
  B_Mbeta = MCMCresult$priors$B_Mbeta
  a_Vsig2 = MCMCresult$priors$a_Vsig2
  b_Vsig2 = MCMCresult$priors$b_Vsig2
  a_Vbeta = MCMCresult$priors$a_Vbeta
  B_Vbeta = MCMCresult$priors$B_Vbeta
  a_pi   = MCMCresult$priors$a_pi
  b_pi   = MCMCresult$priors$b_pi
  a_mu   = MCMCresult$priors$a_mu
  b_mu   = MCMCresult$priors$b_mu
  a_tau2 = MCMCresult$priors$a_tau2
  b_tau2 = MCMCresult$priors$b_tau2
  
  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
  
  rho = runif(n_MCMC)
  
  # End initial values ------------------------------------------------------------
  for (post_reps in 1:n_MCMC) {
    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
    
    rho_mc = rho[post_reps] * rep(1,D)
    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
    alpha_theta = alpha_theta_draws[post_reps]
    alpha_omega = alpha_omega_draws[post_reps]
    
    MCresult = EDPpostmc_concon(p_C1, p_C2,
                                n_k, n_rk, Ky, Kyx, max_Kx_Sy, 
                                D, num_MC, rho_mc,
                                YbetaPars, Ysig2Pars,
                                MbetaPars, Msig2Pars,
                                VbetaPars_array, Vsig2Pars_array,
                                ZpiPars_array, XpiPars_array, 
                                XmuPars_array, Xtau2Pars_array,
                                alpha_theta, alpha_omega, 
                                f0_z0_mc, f0_z1_mc,
                                YbetaPrior_mc, 
                                MbetaPrior_mc, Msig2Prior_mc,
                                VbetaPrior_mc, Vsig2Prior_mc,
                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
    
    M0_mc[[post_reps]] = MCresult$M0_mc
    Mr_mc[[post_reps]] = MCresult$Mr_mc
    M1_mc[[post_reps]] = MCresult$M1_mc
    
    if (post_reps %% iter_check == 0){
      cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
    }
  }
  
  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}

M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)

mean(M)
mean(M[Z==0])
mean(M[Z==1])

# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)

# print("dist. of M based on the data")
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("dist. of M based on the G-computation")
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
abline(v = 0, col = "black", lwd = 2)
abline(v = 1, col = "black", lwd = 2)
legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")

# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = "unif"
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)

NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc

CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c("NIE","NDE","ATE")

NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE

q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col="red",ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col="blue",ylim=ylim_CE);par(new=T)
plot(sort(ATErhoUnif),col="green",ylim=ylim_CE)
CE_tableRhoUnif

```

\newpage
### dist. of f(M) = log(1+M)
```{r}
set.seed(1)
M = LITEdata$att
M = log(1+M)

MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
                              gibbs_iter, gibbs_burnin, gibbs_thin,
                              D, num_MC, num_MC_prior)

{
  # Significance Level alpha
  level = 0.05
  quantile_alpha = c(level/2,1-level/2)
  
  # the number of Gibbs Sampler stored
  n_MCMC = MCMCresult$constants$n_MCMC
  
  # Define interation check
  iter_check = floor(n_MCMC/10)
  
  M0_mc = list(NA)
  Mr_mc = list(NA)
  M1_mc = list(NA)
  
  N = MCMCresult$constants$N
  D = MCMCresult$constants$D
  num_MC = MCMCresult$constants$num_MC
  p_V = MCMCresult$constants$p_V
  p_Z = MCMCresult$constants$p_Z
  p_C1 = MCMCresult$constants$p_C1
  p_C2 = MCMCresult$constants$p_C2
  
  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
  
  a_Ysig2 = MCMCresult$priors$a_Ysig2
  b_Ysig2 = MCMCresult$priors$b_Ysig2
  a_Ybeta = MCMCresult$priors$a_Ybeta
  B_Ybeta = MCMCresult$priors$B_Ybeta
  a_Msig2 = MCMCresult$priors$a_Msig2
  b_Msig2 = MCMCresult$priors$b_Msig2
  a_Mbeta = MCMCresult$priors$a_Mbeta
  B_Mbeta = MCMCresult$priors$B_Mbeta
  a_Vsig2 = MCMCresult$priors$a_Vsig2
  b_Vsig2 = MCMCresult$priors$b_Vsig2
  a_Vbeta = MCMCresult$priors$a_Vbeta
  B_Vbeta = MCMCresult$priors$B_Vbeta
  a_pi   = MCMCresult$priors$a_pi
  b_pi   = MCMCresult$priors$b_pi
  a_mu   = MCMCresult$priors$a_mu
  b_mu   = MCMCresult$priors$b_mu
  a_tau2 = MCMCresult$priors$a_tau2
  b_tau2 = MCMCresult$priors$b_tau2
  
  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
  
  rho = runif(n_MCMC)
  
  # End initial values ------------------------------------------------------------
  for (post_reps in 1:n_MCMC) {
    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
    
    rho_mc = rho[post_reps] * rep(1,D)
    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
    alpha_theta = alpha_theta_draws[post_reps]
    alpha_omega = alpha_omega_draws[post_reps]
    
    MCresult = EDPpostmc_concon(p_C1, p_C2,
                                n_k, n_rk, Ky, Kyx, max_Kx_Sy, 
                                D, num_MC, rho_mc,
                                YbetaPars, Ysig2Pars,
                                MbetaPars, Msig2Pars,
                                VbetaPars_array, Vsig2Pars_array,
                                ZpiPars_array, XpiPars_array, 
                                XmuPars_array, Xtau2Pars_array,
                                alpha_theta, alpha_omega, 
                                f0_z0_mc, f0_z1_mc,
                                YbetaPrior_mc, 
                                MbetaPrior_mc, Msig2Prior_mc,
                                VbetaPrior_mc, Vsig2Prior_mc,
                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
    
    M0_mc[[post_reps]] = MCresult$M0_mc
    Mr_mc[[post_reps]] = MCresult$Mr_mc
    M1_mc[[post_reps]] = MCresult$M1_mc
    
    if (post_reps %% iter_check == 0){
      cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
    }
  }
  
  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}

M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)

mean(M)
mean(M[Z==0])
mean(M[Z==1])

# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)

# print("dist. of M based on the data")
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("dist. of M based on the G-computation")
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
abline(v = 0, col = "black", lwd = 2)
abline(v = 1, col = "black", lwd = 2)
legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")

# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = "unif"
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)

NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc

CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c("NIE","NDE","ATE")

NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE

q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col="red",ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col="blue",ylim=ylim_CE);par(new=T)
plot(sort(ATErhoUnif),col="green",ylim=ylim_CE)
CE_tableRhoUnif

```

\newpage
### dist. of f(M) = invlogit(M)
```{r}
set.seed(1)
M = LITEdata$att

M = as.numeric(scale(M))
M = exp(M)
M = log(1+M)
M = invlogit(M)

eps = 0.1
M = (M*(diff(range(M))-2*eps))+eps

eps = 0.1
M = (M*(diff(range(M))-2*eps))+eps
M = log(M/(1-M))

MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
                              gibbs_iter, gibbs_burnin, gibbs_thin,
                              D, num_MC, num_MC_prior)

{
  # Significance Level alpha
  level = 0.05
  quantile_alpha = c(level/2,1-level/2)
  
  # the number of Gibbs Sampler stored
  n_MCMC = MCMCresult$constants$n_MCMC
  
  # Define interation check
  iter_check = floor(n_MCMC/10)
  
  M0_mc = list(NA)
  Mr_mc = list(NA)
  M1_mc = list(NA)
  
  N = MCMCresult$constants$N
  D = MCMCresult$constants$D
  num_MC = MCMCresult$constants$num_MC
  p_V = MCMCresult$constants$p_V
  p_Z = MCMCresult$constants$p_Z
  p_C1 = MCMCresult$constants$p_C1
  p_C2 = MCMCresult$constants$p_C2
  
  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
  
  a_Ysig2 = MCMCresult$priors$a_Ysig2
  b_Ysig2 = MCMCresult$priors$b_Ysig2
  a_Ybeta = MCMCresult$priors$a_Ybeta
  B_Ybeta = MCMCresult$priors$B_Ybeta
  a_Msig2 = MCMCresult$priors$a_Msig2
  b_Msig2 = MCMCresult$priors$b_Msig2
  a_Mbeta = MCMCresult$priors$a_Mbeta
  B_Mbeta = MCMCresult$priors$B_Mbeta
  a_Vsig2 = MCMCresult$priors$a_Vsig2
  b_Vsig2 = MCMCresult$priors$b_Vsig2
  a_Vbeta = MCMCresult$priors$a_Vbeta
  B_Vbeta = MCMCresult$priors$B_Vbeta
  a_pi   = MCMCresult$priors$a_pi
  b_pi   = MCMCresult$priors$b_pi
  a_mu   = MCMCresult$priors$a_mu
  b_mu   = MCMCresult$priors$b_mu
  a_tau2 = MCMCresult$priors$a_tau2
  b_tau2 = MCMCresult$priors$b_tau2
  
  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
  
  rho = runif(n_MCMC)
  
  # End initial values ------------------------------------------------------------
  for (post_reps in 1:n_MCMC) {
    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
    
    rho_mc = rho[post_reps] * rep(1,D)
    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
    alpha_theta = alpha_theta_draws[post_reps]
    alpha_omega = alpha_omega_draws[post_reps]
    
    MCresult = EDPpostmc_concon(p_C1, p_C2,
                                n_k, n_rk, Ky, Kyx, max_Kx_Sy, 
                                D, num_MC, rho_mc,
                                YbetaPars, Ysig2Pars,
                                MbetaPars, Msig2Pars,
                                VbetaPars_array, Vsig2Pars_array,
                                ZpiPars_array, XpiPars_array, 
                                XmuPars_array, Xtau2Pars_array,
                                alpha_theta, alpha_omega, 
                                f0_z0_mc, f0_z1_mc,
                                YbetaPrior_mc, 
                                MbetaPrior_mc, Msig2Prior_mc,
                                VbetaPrior_mc, Vsig2Prior_mc,
                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
    
    M0_mc[[post_reps]] = MCresult$M0_mc
    Mr_mc[[post_reps]] = MCresult$Mr_mc
    M1_mc[[post_reps]] = MCresult$M1_mc
    
    if (post_reps %% iter_check == 0){
      cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
    }
  }
  
  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}

M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)

mean(M)
mean(M[Z==0])
mean(M[Z==1])

# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)

# print("dist. of M based on the data")
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("dist. of M based on the G-computation")
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
abline(v = 0, col = "black", lwd = 2)
abline(v = 1, col = "black", lwd = 2)
legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")

# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = "unif"
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)

NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc

CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c("NIE","NDE","ATE")

NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE

q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col="red",ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col="blue",ylim=ylim_CE);par(new=T)
plot(sort(ATErhoUnif),col="green",ylim=ylim_CE)
CE_tableRhoUnif

```

\newpage
### dist. of f(M)
```{r}
set.seed(1)
M = LITEdata$att

eps = 0.1
M = (M*(diff(range(M))-2*eps))+eps

MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
                              gibbs_iter, gibbs_burnin, gibbs_thin,
                              D, num_MC, num_MC_prior)

{
  # Significance Level alpha
  level = 0.05
  quantile_alpha = c(level/2,1-level/2)
  
  # the number of Gibbs Sampler stored
  n_MCMC = MCMCresult$constants$n_MCMC
  
  # Define interation check
  iter_check = floor(n_MCMC/10)
  
  M0_mc = list(NA)
  Mr_mc = list(NA)
  M1_mc = list(NA)
  
  N = MCMCresult$constants$N
  D = MCMCresult$constants$D
  num_MC = MCMCresult$constants$num_MC
  p_V = MCMCresult$constants$p_V
  p_Z = MCMCresult$constants$p_Z
  p_C1 = MCMCresult$constants$p_C1
  p_C2 = MCMCresult$constants$p_C2
  
  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
  
  a_Ysig2 = MCMCresult$priors$a_Ysig2
  b_Ysig2 = MCMCresult$priors$b_Ysig2
  a_Ybeta = MCMCresult$priors$a_Ybeta
  B_Ybeta = MCMCresult$priors$B_Ybeta
  a_Msig2 = MCMCresult$priors$a_Msig2
  b_Msig2 = MCMCresult$priors$b_Msig2
  a_Mbeta = MCMCresult$priors$a_Mbeta
  B_Mbeta = MCMCresult$priors$B_Mbeta
  a_Vsig2 = MCMCresult$priors$a_Vsig2
  b_Vsig2 = MCMCresult$priors$b_Vsig2
  a_Vbeta = MCMCresult$priors$a_Vbeta
  B_Vbeta = MCMCresult$priors$B_Vbeta
  a_pi   = MCMCresult$priors$a_pi
  b_pi   = MCMCresult$priors$b_pi
  a_mu   = MCMCresult$priors$a_mu
  b_mu   = MCMCresult$priors$b_mu
  a_tau2 = MCMCresult$priors$a_tau2
  b_tau2 = MCMCresult$priors$b_tau2
  
  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
  
  rho = runif(n_MCMC)
  
  # End initial values ------------------------------------------------------------
  for (post_reps in 1:n_MCMC) {
    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
    
    rho_mc = rho[post_reps] * rep(1,D)
    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
    alpha_theta = alpha_theta_draws[post_reps]
    alpha_omega = alpha_omega_draws[post_reps]
    
    MCresult = EDPpostmc_concon(p_C1, p_C2,
                                n_k, n_rk, Ky, Kyx, max_Kx_Sy, 
                                D, num_MC, rho_mc,
                                YbetaPars, Ysig2Pars,
                                MbetaPars, Msig2Pars,
                                VbetaPars_array, Vsig2Pars_array,
                                ZpiPars_array, XpiPars_array, 
                                XmuPars_array, Xtau2Pars_array,
                                alpha_theta, alpha_omega, 
                                f0_z0_mc, f0_z1_mc,
                                YbetaPrior_mc, 
                                MbetaPrior_mc, Msig2Prior_mc,
                                VbetaPrior_mc, Vsig2Prior_mc,
                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
    
    M0_mc[[post_reps]] = MCresult$M0_mc
    Mr_mc[[post_reps]] = MCresult$Mr_mc
    M1_mc[[post_reps]] = MCresult$M1_mc
    
    if (post_reps %% iter_check == 0){
      cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
    }
  }
  
  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}

M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)

mean(M)
mean(M[Z==0])
mean(M[Z==1])

# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)

# print("dist. of M based on the data")
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("dist. of M based on the G-computation")
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
abline(v = 0, col = "black", lwd = 2)
abline(v = 1, col = "black", lwd = 2)
legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")

# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = "unif"
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)

NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc

CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c("NIE","NDE","ATE")

NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE

q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col="red",ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col="blue",ylim=ylim_CE);par(new=T)
plot(sort(ATErhoUnif),col="green",ylim=ylim_CE)
CE_tableRhoUnif

```

\newpage
### dist. of f(M)
```{r}
set.seed(1)
M = LITEdata$att

eps = 0.1
M = (M*(diff(range(M))-2*eps))+eps
M = log(M/(1-M))

MCMCresult = EDPmediationMCMC(Y, M, V, Z, C,
                              gibbs_iter, gibbs_burnin, gibbs_thin,
                              D, num_MC, num_MC_prior)

{
  # Significance Level alpha
  level = 0.05
  quantile_alpha = c(level/2,1-level/2)
  
  # the number of Gibbs Sampler stored
  n_MCMC = MCMCresult$constants$n_MCMC
  
  # Define interation check
  iter_check = floor(n_MCMC/10)
  
  M0_mc = list(NA)
  Mr_mc = list(NA)
  M1_mc = list(NA)
  
  N = MCMCresult$constants$N
  D = MCMCresult$constants$D
  num_MC = MCMCresult$constants$num_MC
  p_V = MCMCresult$constants$p_V
  p_Z = MCMCresult$constants$p_Z
  p_C1 = MCMCresult$constants$p_C1
  p_C2 = MCMCresult$constants$p_C2
  
  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
  
  a_Ysig2 = MCMCresult$priors$a_Ysig2
  b_Ysig2 = MCMCresult$priors$b_Ysig2
  a_Ybeta = MCMCresult$priors$a_Ybeta
  B_Ybeta = MCMCresult$priors$B_Ybeta
  a_Msig2 = MCMCresult$priors$a_Msig2
  b_Msig2 = MCMCresult$priors$b_Msig2
  a_Mbeta = MCMCresult$priors$a_Mbeta
  B_Mbeta = MCMCresult$priors$B_Mbeta
  a_Vsig2 = MCMCresult$priors$a_Vsig2
  b_Vsig2 = MCMCresult$priors$b_Vsig2
  a_Vbeta = MCMCresult$priors$a_Vbeta
  B_Vbeta = MCMCresult$priors$B_Vbeta
  a_pi   = MCMCresult$priors$a_pi
  b_pi   = MCMCresult$priors$b_pi
  a_mu   = MCMCresult$priors$a_mu
  b_mu   = MCMCresult$priors$b_mu
  a_tau2 = MCMCresult$priors$a_tau2
  b_tau2 = MCMCresult$priors$b_tau2
  
  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
  
  rho = runif(n_MCMC)
  
  # End initial values ------------------------------------------------------------
  for (post_reps in 1:n_MCMC) {
    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
    
    rho_mc = rho[post_reps] * rep(1,D)
    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
    alpha_theta = alpha_theta_draws[post_reps]
    alpha_omega = alpha_omega_draws[post_reps]
    
    MCresult = EDPpostmc_concon(p_C1, p_C2,
                                n_k, n_rk, Ky, Kyx, max_Kx_Sy, 
                                D, num_MC, rho_mc,
                                YbetaPars, Ysig2Pars,
                                MbetaPars, Msig2Pars,
                                VbetaPars_array, Vsig2Pars_array,
                                ZpiPars_array, XpiPars_array, 
                                XmuPars_array, Xtau2Pars_array,
                                alpha_theta, alpha_omega, 
                                f0_z0_mc, f0_z1_mc,
                                YbetaPrior_mc, 
                                MbetaPrior_mc, Msig2Prior_mc,
                                VbetaPrior_mc, Vsig2Prior_mc,
                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
    
    M0_mc[[post_reps]] = MCresult$M0_mc
    Mr_mc[[post_reps]] = MCresult$Mr_mc
    M1_mc[[post_reps]] = MCresult$M1_mc
    
    if (post_reps %% iter_check == 0){
      cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
    }
  }
  
  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}

M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)

mean(M)
mean(M[Z==0])
mean(M[Z==1])

# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)

# print("dist. of M based on the data")
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("dist. of M based on the G-computation")
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
abline(v = 0, col = "black", lwd = 2)
abline(v = 1, col = "black", lwd = 2)
legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")

# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = "unif"
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)

NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc

CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c("NIE","NDE","ATE")

NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE

q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col="red",ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col="blue",ylim=ylim_CE);par(new=T)
plot(sort(ATErhoUnif),col="green",ylim=ylim_CE)
CE_tableRhoUnif

```

\newpage
### dist. of f(M)
```{r}
set.seed(1)
M = LITEdata$att

YY = c(Y,Y+rnorm(N,0,0.1))
MM = c(M,M)
VV = c(V,V+rnorm(N,0,0.1))
ZZ = c(Z,Z)

p_C = ncol(C)
p_C1 = sum(apply(C, 2, function(x) { all(x %in% 0:1) }))
p_C2 = p_C - p_C1
AA = rbind(C,C)
AA[(N+1):(2*N),((p_C1+1):p_C)] = AA[(N+1):(2*N),((p_C1+1):p_C)] + matrix(rnorm(p_C2*N,0,0.1),ncol=p_C2)
CC = AA

MCMCresult = EDPmediationMCMC(YY, MM, VV, ZZ, CC,
                              gibbs_iter, gibbs_burnin, gibbs_thin,
                              D, num_MC, num_MC_prior)

{
  # Significance Level alpha
  level = 0.05
  quantile_alpha = c(level/2,1-level/2)
  
  # the number of Gibbs Sampler stored
  n_MCMC = MCMCresult$constants$n_MCMC
  
  # Define interation check
  iter_check = floor(n_MCMC/10)
  
  M0_mc = list(NA)
  Mr_mc = list(NA)
  M1_mc = list(NA)
  
  N = MCMCresult$constants$N
  D = MCMCresult$constants$D
  num_MC = MCMCresult$constants$num_MC
  p_V = MCMCresult$constants$p_V
  p_Z = MCMCresult$constants$p_Z
  p_C1 = MCMCresult$constants$p_C1
  p_C2 = MCMCresult$constants$p_C2
  
  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
  
  a_Ysig2 = MCMCresult$priors$a_Ysig2
  b_Ysig2 = MCMCresult$priors$b_Ysig2
  a_Ybeta = MCMCresult$priors$a_Ybeta
  B_Ybeta = MCMCresult$priors$B_Ybeta
  a_Msig2 = MCMCresult$priors$a_Msig2
  b_Msig2 = MCMCresult$priors$b_Msig2
  a_Mbeta = MCMCresult$priors$a_Mbeta
  B_Mbeta = MCMCresult$priors$B_Mbeta
  a_Vsig2 = MCMCresult$priors$a_Vsig2
  b_Vsig2 = MCMCresult$priors$b_Vsig2
  a_Vbeta = MCMCresult$priors$a_Vbeta
  B_Vbeta = MCMCresult$priors$B_Vbeta
  a_pi   = MCMCresult$priors$a_pi
  b_pi   = MCMCresult$priors$b_pi
  a_mu   = MCMCresult$priors$a_mu
  b_mu   = MCMCresult$priors$b_mu
  a_tau2 = MCMCresult$priors$a_tau2
  b_tau2 = MCMCresult$priors$b_tau2
  
  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
  
  rho = runif(n_MCMC)
  
  # End initial values ------------------------------------------------------------
  for (post_reps in 1:n_MCMC) {
    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
    
    rho_mc = rho[post_reps] * rep(1,D)
    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
    alpha_theta = alpha_theta_draws[post_reps]
    alpha_omega = alpha_omega_draws[post_reps]
    
    MCresult = EDPpostmc_concon(p_C1, p_C2,
                                n_k, n_rk, Ky, Kyx, max_Kx_Sy, 
                                D, num_MC, rho_mc,
                                YbetaPars, Ysig2Pars,
                                MbetaPars, Msig2Pars,
                                VbetaPars_array, Vsig2Pars_array,
                                ZpiPars_array, XpiPars_array, 
                                XmuPars_array, Xtau2Pars_array,
                                alpha_theta, alpha_omega, 
                                f0_z0_mc, f0_z1_mc,
                                YbetaPrior_mc, 
                                MbetaPrior_mc, Msig2Prior_mc,
                                VbetaPrior_mc, Vsig2Prior_mc,
                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
    
    M0_mc[[post_reps]] = MCresult$M0_mc
    Mr_mc[[post_reps]] = MCresult$Mr_mc
    M1_mc[[post_reps]] = MCresult$M1_mc
    
    if (post_reps %% iter_check == 0){
      cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
    }
  }
  
  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}

M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)

mean(M)
mean(M[Z==0])
mean(M[Z==1])

# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)

# print("dist. of M based on the data")
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("dist. of M based on the G-computation")
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
abline(v = 0, col = "black", lwd = 2)
abline(v = 1, col = "black", lwd = 2)
legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")

# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = "unif"
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)

NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc

CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c("NIE","NDE","ATE")

NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE

q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col="red",ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col="blue",ylim=ylim_CE);par(new=T)
plot(sort(ATErhoUnif),col="green",ylim=ylim_CE)
CE_tableRhoUnif

```

\newpage
### dist. of f(M)
```{r}
set.seed(1)
M = LITEdata$att

YY = c(Y,Y+rnorm(N,0,0.1),Y+rnorm(N,0,0.1),Y+rnorm(N,0,0.1))
MM = c(M,M,M,M)
VV = c(V,V+rnorm(N,0,0.1),V+rnorm(N,0,0.1),V+rnorm(N,0,0.1))
ZZ = c(Z,Z,Z,Z)

p_C = ncol(C)
p_C1 = sum(apply(C, 2, function(x) { all(x %in% 0:1) }))
p_C2 = p_C - p_C1
AA = rbind(C,C,C,C)
AA[(N+1):(4*N),((p_C1+1):p_C)] = AA[(N+1):(4*N),((p_C1+1):p_C)] + matrix(rnorm((p_C2*3*N),0,0.1),ncol=p_C2)
CC = AA

MCMCresult = EDPmediationMCMC(YY, MM, VV, ZZ, CC,
                              gibbs_iter, gibbs_burnin, gibbs_thin,
                              D, num_MC, num_MC_prior)

{
  # Significance Level alpha
  level = 0.05
  quantile_alpha = c(level/2,1-level/2)
  
  # the number of Gibbs Sampler stored
  n_MCMC = MCMCresult$constants$n_MCMC
  
  # Define interation check
  iter_check = floor(n_MCMC/10)
  
  M0_mc = list(NA)
  Mr_mc = list(NA)
  M1_mc = list(NA)
  
  N = MCMCresult$constants$N
  D = MCMCresult$constants$D
  num_MC = MCMCresult$constants$num_MC
  p_V = MCMCresult$constants$p_V
  p_Z = MCMCresult$constants$p_Z
  p_C1 = MCMCresult$constants$p_C1
  p_C2 = MCMCresult$constants$p_C2
  
  f0_z0_mc = MCMCresult$MCpriors$f0_z0_mc
  f0_z1_mc = MCMCresult$MCpriors$f0_z1_mc
  YbetaPrior_mc = MCMCresult$MCpriors$YbetaPrior_mc
  MbetaPrior_mc = MCMCresult$MCpriors$MbetaPrior_mc
  Msig2Prior_mc = MCMCresult$MCpriors$Msig2Prior_mc
  VbetaPrior_mc = MCMCresult$MCpriors$VbetaPrior_mc
  Vsig2Prior_mc = MCMCresult$MCpriors$Vsig2Prior_mc
  
  a_Ysig2 = MCMCresult$priors$a_Ysig2
  b_Ysig2 = MCMCresult$priors$b_Ysig2
  a_Ybeta = MCMCresult$priors$a_Ybeta
  B_Ybeta = MCMCresult$priors$B_Ybeta
  a_Msig2 = MCMCresult$priors$a_Msig2
  b_Msig2 = MCMCresult$priors$b_Msig2
  a_Mbeta = MCMCresult$priors$a_Mbeta
  B_Mbeta = MCMCresult$priors$B_Mbeta
  a_Vsig2 = MCMCresult$priors$a_Vsig2
  b_Vsig2 = MCMCresult$priors$b_Vsig2
  a_Vbeta = MCMCresult$priors$a_Vbeta
  B_Vbeta = MCMCresult$priors$B_Vbeta
  a_pi   = MCMCresult$priors$a_pi
  b_pi   = MCMCresult$priors$b_pi
  a_mu   = MCMCresult$priors$a_mu
  b_mu   = MCMCresult$priors$b_mu
  a_tau2 = MCMCresult$priors$a_tau2
  b_tau2 = MCMCresult$priors$b_tau2
  
  alpha_theta_draws = MCMCresult$MCMCposteriors$alpha_theta_draws
  alpha_omega_draws = MCMCresult$MCMCposteriors$alpha_omega_draws
  
  rho = runif(n_MCMC)
  
  # End initial values ------------------------------------------------------------
  for (post_reps in 1:n_MCMC) {
    Ky = MCMCresult$MCMCposteriors$KyLists[[post_reps]]
    Kyx = MCMCresult$MCMCposteriors$KyxLists[[post_reps]]
    n_k = MCMCresult$MCMCposteriors$n_kLists[[post_reps]]
    n_rk = MCMCresult$MCMCposteriors$n_rkLists[[post_reps]]
    max_Kx_Sy = MCMCresult$MCMCposteriors$max_Kx_SyLists[[post_reps]]
    
    rho_mc = rho[post_reps] * rep(1,D)
    YbetaPars = MCMCresult$MCMCposteriors$YbetaLists[[post_reps]]
    Ysig2Pars = MCMCresult$MCMCposteriors$Ysig2Lists[[post_reps]]
    MbetaPars = MCMCresult$MCMCposteriors$MbetaLists[[post_reps]]
    Msig2Pars = MCMCresult$MCMCposteriors$Msig2Lists[[post_reps]]
    VbetaPars_array = MCMCresult$MCMCposteriors$VbetaLists[[post_reps]]
    Vsig2Pars_array = MCMCresult$MCMCposteriors$Vsig2Lists[[post_reps]]
    ZpiPars_array   = MCMCresult$MCMCposteriors$ZpiLists[[post_reps]]
    XpiPars_array   = MCMCresult$MCMCposteriors$XpiLists[[post_reps]]
    XmuPars_array   = MCMCresult$MCMCposteriors$XmuLists[[post_reps]]
    Xtau2Pars_array = MCMCresult$MCMCposteriors$Xtau2Lists[[post_reps]]
    alpha_theta = alpha_theta_draws[post_reps]
    alpha_omega = alpha_omega_draws[post_reps]
    
    MCresult = EDPpostmc_concon(p_C1, p_C2,
                                n_k, n_rk, Ky, Kyx, max_Kx_Sy, 
                                D, num_MC, rho_mc,
                                YbetaPars, Ysig2Pars,
                                MbetaPars, Msig2Pars,
                                VbetaPars_array, Vsig2Pars_array,
                                ZpiPars_array, XpiPars_array, 
                                XmuPars_array, Xtau2Pars_array,
                                alpha_theta, alpha_omega, 
                                f0_z0_mc, f0_z1_mc,
                                YbetaPrior_mc, 
                                MbetaPrior_mc, Msig2Prior_mc,
                                VbetaPrior_mc, Vsig2Prior_mc,
                                a_Ysig2, b_Ysig2, a_Ybeta, B_Ybeta,
                                a_Msig2, b_Msig2, a_Mbeta, B_Mbeta,
                                a_Vsig2, b_Vsig2, a_Vbeta, B_Vbeta,
                                a_pi, b_pi, a_mu, b_mu, a_tau2, b_tau2)
    
    M0_mc[[post_reps]] = MCresult$M0_mc
    Mr_mc[[post_reps]] = MCresult$Mr_mc
    M1_mc[[post_reps]] = MCresult$M1_mc
    
    if (post_reps %% iter_check == 0){
      cat("Post-Processing",post_reps,"(",(post_reps/n_MCMC)*100,"%)","Time:",date(),"\n")
    }
  }
  
  distM = list(M0_mc = M0_mc, Mr_mc = Mr_mc, M1_mc = M1_mc)
}

M0_mc = unlist(distM$M0_mc)
Mr_mc = unlist(distM$Mr_mc)
M1_mc = unlist(distM$M1_mc)

mean(M)
mean(M[Z==0])
mean(M[Z==1])

# n = MCMCresult$constants$D
n = 1e5
ylim_CE = c( 0.0, 2.0)
xlim_CE = c(min(M)-1, max(M)+1)

# print("dist. of M based on the data")
plot(density(M,n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(M[Z==0],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M[Z==1],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Data",col="green")
legend("topright", legend=c("M", "M[Z==0]", "M[Z==1]"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("dist. of M based on the G-computation")
ylim_CE = c( 0.0, 2.0)
plot(density(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="red");par(new=T)
plot(density(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="",col="blue");par(new=T)
plot(density(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],n=n),xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="G-computation",col="green")
abline(v = 0, col = "black", lwd = 2)
abline(v = 1, col = "black", lwd = 2)
legend("topright", legend=c("M0", "Mr", "M1"), col=c("red", "blue", "green"), 
       lty=rep(1,3), cex=1, text.font=4)

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 100)
hist(M,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M: data")
hist(M[Z==0],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==0]: data")
hist(M[Z==1],xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M[Z==1]: data")

# print("histogram of M based on the G-computation")
ylim_CE = c( 0.0, 350)
hist(M0_mc[which((M0_mc>xlim_CE[1])*(M0_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M0: G-computation")
hist(Mr_mc[which((Mr_mc>xlim_CE[1])*(Mr_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="Mr: G-computation")
hist(M1_mc[which((M1_mc>xlim_CE[1])*(M1_mc<xlim_CE[2])==1)],1e3,xlim=xlim_CE,ylim=ylim_CE,xlab="",ylab="",main="M1: G-computation")

# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
rho = "unif"
POSTresultRhoUnif = EDPmediationPOST(MCMCresult, esttype, rho, save_cluster)

NIE_tableRhoUnif = POSTresultRhoUnif$NIE_result_mc
NDE_tableRhoUnif = POSTresultRhoUnif$NDE_result_mc
ATE_tableRhoUnif = POSTresultRhoUnif$ATE_result_mc

CE_tableRhoUnif = rbind(NIE_tableRhoUnif,NDE_tableRhoUnif,ATE_tableRhoUnif)
rownames(CE_tableRhoUnif) = c("NIE","NDE","ATE")

NIErhoUnif = POSTresultRhoUnif$NIE
NDErhoUnif = POSTresultRhoUnif$NDE
ATErhoUnif = POSTresultRhoUnif$ATE

q95 = quantile(c(NIErhoUnif,NDErhoUnif,ATErhoUnif),c(0.025, 0.975))
ylim_CE=c(floor(min(q95)),ceiling(max(c(q95))))
plot(sort(NIErhoUnif),col="red",ylim=ylim_CE);par(new=T)
plot(sort(NDErhoUnif),col="blue",ylim=ylim_CE);par(new=T)
plot(sort(ATErhoUnif),col="green",ylim=ylim_CE)
CE_tableRhoUnif

```